Geometry

• AAA, ASS, SSA Theorems [Zakiyah, 11/16/2001]
  Why can't AAA, ASS, and SSA be used to determine triangle congruence?

• About Basic Geometry [Santiago, 10/14/1998]
  Who developed basic geometry? What is it used for? Who uses it?

• Accuracy in Measurement [Rosemary, 02/08/2002]
  Since pi is irrational, either the circumference or the diameter of a circle must be irrational. How is that possible?

• Alternate and Corresponding Angles [Battersby, 10/21/1996]
  Please explain corresponding and alternate angles.

• Angle Inscribed in a Semicircle [Sondra, 11/07/2001]
  Prove that any angle inscribed in a semicircle is a right angle.

• Angle-Side-Side Does Not Work [Dana, 11/12/2001]
  Can you give me a construction to show that Angle-Side-Side does not prove two triangles congruent?

• Another Grazing Cow [Ryland, 6/7/1995]
  A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing?

• Area and Volume of a Football [Heinrichs, 3/28/1995]
  How would one find the area of a football? Or then again, how would one find the volume of a football?

• Area of an Ellipse [Dault, 11/4/1996]
  How do you find the area of an ellipse?

• Area of an Octagon [Brad, 10/26/2001]
  I am trying to figure out the square footage of an octagon-shaped house. Each wall measures 15 ft. in length.

• Arrange 7 Points in a Plane... [Lesko, 10/05/1998]
  Arrange 7 points in a plane so that if any three are chosen, at least 2 of them will be a unit distance apart.

• Building a Geometric Proof [Karen, 06/03/1999]
  Can you explain how to do a two-column proof?

• Building Two Column Proofs [Crystal, 09/12/1998]
  We just started learning proofs, and I don't understand how to figure out the ordering. Can you explain?

• Circle Inscribed in Triangle [Willydog, 04/04/1997]
  What is the radius of a circle inscribed in a 3-4-5 right triangle?

• Circles Inscribed in Triangles [Moltay, 11/14/1996]
  Given two triangles, prove that r1 + r2 + r3 = r.

• A Complete Proof about Tangential Circles [Emma, 06/05/1998]
  Can you show me a proof, with full justification, of the following theorem? Two circles of the same radius touch at A ...

• Congruence and Triangles [Soarees, 12/13/1997]
  Can you please explain how to determine, using SSS, SAS, and ASA, how a shape is congruent or not?

• Congruent Triangles in a Rectangle [Lacey, 11/11/1999]
  Given rectangle BART with AB parallel to RT, AR perpendicular to AB, BT perpendicular to RT, AB congruent to RT, and AR congruent to TB, how can I prove that triangle ABR is congruent to triangle TRB?

• Constructing Polygons [Grant, 06/03/1998]
  How do you construct a regular pentagon and a regular decagon? Can you construct a regular n-gon?

• Constructing a Square [Poleshuck, 12/25/1998]
  Given any four points, construct a square such that each side or extension passes through one point.

• Curious Property of a Regular Heptagon [McCready, 04/06/2001]
  How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/ AD)?

• Defining Distance Mathematically [Chanet, 10/16/1996]
  What is wrong with D' = sqrt(X^2 - X'2)?

• Definition of Opposite Sides [Stortz, 01/18/2001]
  What is the formal definition of 'opposite sides' of a polygon? Does a regular pentagon have opposite sides? Does a concave polygon have opposite sides? How can we define it consistent with our intuition?

• Deriving the Dot Product [Nick, 09/17/1998]
  Can you explain how to derive formula for the dot product?

• Determining Triangle Similarity [Big Red, 05/26/1998]
  Given two triangles, how can you determine if they are similar?

• Diagonals and Tiles [Kamie, 11/17/2001]
  Jay tiled a 15x21' rectangular ballroom with 1 ft. sq. tiles. Then he drew diagonals connecting opposite corners of the room. How many tiles did the diagonals pass through?

• Diagonals in 3D Figures [Vassallo, 06/21/1999]
  Could you help me develop a formula for determining the number of diagonals in various 3D figures, especially pyramids and prisms?

• Diameter of Flying Saucer [Mudobber, 5/27/1996]
  We are constructing an oval racetrack in Atlanta...

• Distance using Latitude and Longitude [Reed, 12/31/1997]
  Is there a simple formula for calculating distance using known latitude and longitude?

• Does a Cone have an Edge? A Vertex? [Mark, 03/12/2002]
  Our 4th grade math textbook defines a cone as "A solid figure with one circular face and one vertex." This sounds reasonable until you read the textbook's definitions for face, edge, and vertex.

• Eleven Nets of a Cube [Ashuk, 11/15/2001]
  My teacher says that there are 11 combinations to make a cube without reversing them, but I can only find 6.

• Fourth Dimension [Zeto, 05/13/1997]
  Can you help me understand the fourth dimension?

• Frustum of a Cone [Blackburn, 12/09/1996]
  If you cut a cone and then lay it out on a flat surface, what will be the inside and outside sizes of this flattened-out cone?

• General Area Formula [Will, 02/14/2002]
  Is there an all-inclusive formula for the area of a square, rectangle, parallelogram, trapezoid, and triangle?

• Geodesics [Matz, 12/15/1996]
  Can you give me information on the math behind geodesics?

• Geometric Proof of Heron's Formula [Lloyd, 01/25/2000]
  How can I prove Hero(n)'s formula using a circle with center P and radius R inscribed in triangle ABC?

• Geometry Class [Miller, 9/2/1996]
  How can I survive my first year of high school geometry?

• Geometry Constructions with Compass and Straightedge [Zaidi, 11/13/1998]
  I need help constructing medians, angle bisectors, and perpendicular bisectors of triangles.

• Geometry Proofs [Victoria, 11/07/2001]
  General and specific advice for a student having trouble writing proofs on her own.

• Geometry vs. Trigonometry [Tipledan, 07/14/1997]
  What is the difference between trigonometry and geometry?

• Hands of a Clock [Porter, 10/10/1997]
  How many times do the hour and minute hands cross in a 12-hour period of time?

• Handshakes and Polygon Diagonals [Brendan, 09/12/2001]
  If a polygon has 42 sides, how many diagonals does it have?

• Heron's Formula, Cartesian Coordinate Plane [Jacob, 11/01/2001]
  If a triangle has sides 5, 6, and the square root of thirteen, what is the area of the triangle?

• How do you get the volume equations for a sphere and pyramid? [Maggiano, 6/10/1996]
  Can you give me the formulas for the volume of a sphere and the volume of a pyramid?

• How to Build a Proof [Veronica, 05/18/1999]
  Given: Triangle ABC is a right triangle... Prove: Angle A and angle B are complementary angles.

• HyperCubes [Mabbott, 3/21/1996]
  Do you folks know of any videos that show the hyper-cube in action that would be appropriate for the high school level?

• Inclusive vs. Exclusive Definitions [Logan, 01/24/2002]
  My geometry teacher says that a square is not also a rhombus, a rectangle, and a parallelogram. Please help!

• Information About Topology [Prakash, 11/12/1996]
  Where can I learn more about topology?

• Is a Sphere 2-D or 3-D? [Janice, 8/8/1996]
  Is a sphere a two- or a three-dimensional object?

• Jobs That Use Geometry [Keesha, 12/18/2001]
  I would like to learn how geometry is used in real life. What jobs involve geometry?

• Length of a Triangle's Sides [Rappard, 1/23/1995]
  I have a triangle problem for you to solve: The lengths of the three sides of a triangle could be...

• Locus and Equations of Lines [Marguerite, 01/10/1999]
  Describe the locus of points that are 3 units from the line x = -1...

• Mathematics and Intuition [Archer, 07/10/2001]
  Certain "puzzlers" in mathematical recreations defy our sense of experience, leaving you wondering if the answer to a problem can really be true. How to convince the intelligent non-believer?

• Maximum Fenced Area, One Side a Barn [Molly, 10/16/2001]
  Solve: y = 70x - 2x^2: find the maximum fenced area if one side is a barn. Why is the rectangle made up of two equal squares?

• Measuring Angles with a Protractor [Rezzi, 02/28/2002]
  I want to know how to measure acute, reflex and obtuse angles with a protractor.

• Moebius Strip [Portal, 8/14/1995]
  Dr. Math, I know what a Moebius strip is, but I forget how to define its unique physical property. Could you please help?

• Non-Algebraic Explanation of a Parabola [Donelle, 05/16/2000]
  What does a parabola look like? How is it formed?

• Number of Cylinder Edges [David, 04/01/2002]
  My son was asked "how many edges are there on a solid cylinder?" on a recent math examination. His answer was "2" and it was marked incorrect.

• Number of Squares in an NxN Square [Fengh, 7/29/1996]
  How many squares are there in an 8 x 8 square? How many rectangles are there?

• One Circle Revolving Around Another [Aumueller, 05/26/1999]
  How many revolutions will a smaller circle make while rotating around the perimeter of a larger circle?

• Only Five Platonic Solids [Demirel, 03/05/1998]
  Why there are only five platonic solids?

• Packing Pennies in a Jar [Gibson, 06/08/1999]
  If a jar has a height of 11" and a radius of 7" and is full of pennies evenly to the top, how many pennies can fit in it?

• Parallel Lines: Euclidean and Non-Euclidean Geometry [Dennis, 4/25/1996]
  If two lines are parallel, can they intersect?

• Parallel Lines: Two Column Proof [Turtle, 09/09/1998]
  Could you break down the steps in doing a two column proof to show that two lines are parallel given certain congruent angles?

• Planes and Lines [Tao, 10/26/1996]
  Do planes and lines contain the same number of points?

• Polyominoes [Wiahome, 09/08/1997]
  I am using polyominos, but I do not know how to tell my dad what they are. How can I tell him so he will know?

• Possible Areas of a Triangle [Sahil, 12/27/2001]
  Exploring the areas of a triangle with side lengths 6 and 7.

• Proof of Congruency [Ledoux, 10/13/1996]
  Line PR bisects angles QPS and QRS; prove that segments RQ and RS are congruent.

• Proving the Pythagorean Theorem [Adams, 04/14/1997]
  I know that the Pythagorean Theorem works and I can show how it works, but why does it work?

• Pythagorean Proof Based on Principles of Scaling [Charlene, 04/04/2002]
  I've decided to do a project with some connections to the Pythagorean theorem, but the project requires innovative ideas.

• Pythagorean Theorem [Bethune, 10/7/1996]
  I don't understand the Pythagorean Theorem.

• The Pythagorean Theorem [Noelle, 07/07/1997]
  Could you please explain the Pythagorean Theorem?

• Pythagorean Theorem and non-Right Triangles [Katy, 03/09/2002]
  Why doesn't the Pythagorean theorem work for triangles other than right triangles?

• Pythagorean Triples [Levin, 10/07/1997]
  What is a Pythagorean triple?

• Round Robin Tournament Schedule [Kinley, 03/31/2000]
  Is there a systematic way to come up with a schedule for a round robin tournament for up to 32 teams, where each team plays every other team once?

• Squaring the Circle [Deloach, 12/22/1997]
  Can you construct a square at all with the same area as a circle with a given radius?

• SSA Theorem: Valid or Invalid? [Chip, 12/19/2001]
  Why can't the SSA Theorem be used to prove congruence?

• Tangent Circle Construction [Midland, 12/02/1996]
  Given a circle with two points inside it, construct another circle that passes through the given points and is tangent to the given circle.

• Tesseracts and Hypercubes [Smith, 05/22/1997]
  Can you give me any good sources of information that a high school geometry student would understand?

• Thinking About Proofs [Erika, 09/24/1997]
  How do you know what statement to write next in a proof? What reasons do you use?

• Three-dimensional Plane Diagrams [Lindsay, 03/10/1999]
  Draw: two parallel planes with another plane intersecting them; two parallel planes with an intersecting line.

• Triangles in a Polygon [Krishna, 06/14/1997]
  A regular 18-sided polygon is inscribed in a circle and triangles are formed by joining any three of the eighteen vertices. How many obtuse triangles are there?

• Trisecting an Angle [Henson, 11/21/1996]
  Is there a proof that you can't trisect an angle?

• Two-column proofs [Osterbur, 12/18/1994]
  I am writing on behalf of my daughter Mel who is a sophomore in high school. She is having a real problem with proofs. In particular two column proofs. Can you explain the steps to prove geometric figures?

• Two-Column Proof: Parallel Tangents [Andrea, 03/08/2002]
  Prove that tangents to a circle at the endpoints of a diameter are parallel.

• Unproven Fundamentals of Geometry [Han, 05/18/1999]
  What are some important postulates or axioms that geometry cannot exist without, but cannot prove, either?

• Volume of a Cylindrical Tank [Blockwook, 2/3/1995]
  I have to keep an inventory of how much is kept in a farm of tanks outside my school. The tanks are cylindrical, which would be no problem if the were standing on end...

• Volume of a Pyramid [Aoun, 05/16/1999]
  Can you give a step-by-step proof for the volume of a pyramid?

• What Are Proofs? [Schmit, 08/12/1997]
  I am homeschooling and do not understand proofs. Can you help me out?

• What is a Cuboctahedron? [Tiana, 01/02/2001]
  What is a cuboctahedron?

• What is Menelaus' Theorem? [Bob, 11/15/1998]
  Proof of Menelaus' Theorem, and discussion of its converse and Desargues' Theorem.

• What is a point? [Hooper, 8/26/1996]
  Define a point, please.

• What is a Theorem and Why are they Important? [Kristin, 08/15/1997]
  I don't understand how theorems help us learn.

• When is a Slope 0 or Undefined? [Purple, 03/29/1997]
  How do I know when the slope of an equation is zero or undefined (no slope)?

• 3d Distance [Leiker, 11/1/1994]
  What's the easiest way to find the distance between a point and a line in three dimensions: When the line is defined by two points in space, and when the line is defined by angles from the cartesian axes?

• Cow Grazing in Circles [Phillips, 11/3/1994]
  A cow is tied to a 100 ft. rope attached to a pole in the center of a circle of radius 50 ft. This circle has a ten foot opening, out of which the cow can walk to graze. What's the grazing area ?

• Geometry: Minimum Distances and Circles [Chang, 11/3/1994]
  Given an arbitrary circle with two arbitrary points A and B within it, using compass and ruler only, is there a way to find a point C on the circle such that the sum of the length AB and the length BC is a minimum?

• Complex shapes [Sledd, 11/3/1994]
  Please describe how to come up with mathematical "descriptions" for complex shapes (torus, witches hat, etc.) using three-dimensional math.

• Test for Point Inside Triangle [Techaumnat, 11/4/1994]
  I have one geometry problem and want a simple solution that can be solved by computer program with good resolution. How can I know that if a point P(x,y) is in a triangle P1(x1,y1) - P2(x2,y2) - P3(x3,y3)?

• Area of a Cone [Bornstein, 11/5/1994]
  What is the area of a cone when given the height and the angle at the convergence point?

• Goat tied to a barn [Thompson, 11/8/1994]
  If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? Assume the goat is tied to a corner.

• Bouncing Balls [Heath, 11/14/1994]
  Geometry Project - Problem: Balls bounce off of solid objects. Is there a pattern to the bounce? Can you predict the bounce?

• Vertical angles [CRBOE, 11/15/1994]
  Are vertical angles congruent in Euclidean geometry?

• Trisecting an angle [CRBOE, 11/16/1994]
  I have been faced with the geometric construction problem of trisecting an angle using only a compass and a straightedge. How is this done?

• Group theory [Baker, 11/22/1994]
  The four rotational symmetries of the square satisfy the four requirements for a group, and so they are called a subgroup of the full symmetry group. (Notice that the identity is one of these rotational symmetries and that the product of two rotations is another rotation in the subgroup.) a. Do the four line symmetries of the square form a subgroup? b. Does the symmetry group of the equilateral triangle have a subgroup?

• Maximization problem [Thacker, 11/29/1994]
  A window is to have the shape of a rectangle topped by a semi-circle. Suppose that the semi-circle part of the window admits one-half as much light per square foot as does the rectangular part. What are the dimensions x and y of the window admitting the most light?

• Ratio and proportion [Gonzalez, 12/5/1994]
  I need extra help in ratio and proportion.

• Chanukah hexagons [Holl, 12/12/1994]
  I gave the students the Star of David for Chanukah. We tried to find all the triangles, quadrilaterals, and hexagons in this star. We were stumped with the number of hexagons. Can you help?

• Definition of an Ellipse [Lu, 1/4/1995]
  I have a question concerning the concept of an ellipse. It is said that the equation for an ellipse is Pf + Pr= 2a where P is a point on the ellipse and f and r are the points of the foci. How do we know that this is true, that is that Pf + Pr = 2a? How did we come up with the constant of 2a?

• The Meteorologists' Theorem [Nishisaka, 1/6/1995]
  Prove the "Meteorologists' Theorem": At any given moment, there are two diametrically opposite points on the (spherical?) Earth's surface where the temperatures are equal and the barometric pressure are equal.

• Quadrilaterals and Diagonals [Mabbott, 1/18/1995]
  If the diagonals of a quad are congruent, must the quad be a rectangle or an isosceles trapezoid?

• Number of Faces of a Cylinder and a Cone [Douglas, 1/29/1995]
  If you have a cylinder, how many faces does it have? What about a cone?

• Word Problems [Backman, 2/1/1995]
  I am totally stumped on these two word problems. They are driving me crazy!

• Euclid's Parallel Postulate [Byram Hills, 2/14/1995]
  We are studying Euclid's Parallel Postulate. Why did mathematicians disagree with him? What other geometries resulted from this disagreement? What postulate replaced the Parallel Postulate?

• Triangle Proof [Michelle, 2/18/1995]
  I'm thinking that maybe to figure it out, it needs to be said that if 2 sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the longer side. I'm not sure how to say it in a proof.

• Constructing a Regular Pentagon [Robbins, 2/21/1995]
  We are interested in knowing how to construct a regular pentagon using a compass and a straight edge.

• What is the Area Not Shared by the Circles? [Basse, 3/3/1995]
  Two circles intersect such that their centers and their points of intersection form a square with each side equal to 3. What is the total area of the sections of the square that are not shared by both circles?

• What does Angle ABC Equal? [Cumyn, 3/5/1995]
  A triangle, ABC, is obtuse angled at C. The bisectors of the exterior angles at A and B meet BC and AC produced at D and E respectively. If AB=AD=BE, then what does angle ABC equal?

• Break a dowel to form a triangle [Chen, 3/8/1995]
  A wooden dowel is randomly broken in 2 places. What is the probability that the 3 resulting fragments can be used to form the sides of a triangle?

• Congruency Theorems for Triangles [Gillies, 3/13/1995]
  Two triangles, one which has two sides that are of equal length to the second triangle, and both having an angle (not contained) equal, cannot be proved congruent. It seems to me that they are congruent, though. Any thoughts on this?

• Conic Sections and Parallel Lines [Howley, 3/18/1995]
  Our teacher told us there was a way to cut a cone with a plane to get parallel lines. Another teacher in the department can do it algebraically, but no one can do it physically. Is there such a plane in reality or only in theory?

• Spreadsheet to Prove that A = pi*r^2 [Smith, 3/18/1995]
  I need to prepare a spreadsheet using repetitive calculations to prove that A = pi*r^2. Help!

• Five Noncollinear Points [Gomez, 4/2/1995]
  In general, how many undirected lines and how many circles are determined by five noncollinear points?

• Find Angle DEA and Angle ADB [Rider, 4/28/1995]
  Given that line AB is parallel to line DC, measure of arc CB=62, measure of angle DAB=104. Find the measure of angle DEA and the measure of angle ADB, and WHY.

• Quadrilateral Problem [Gheorghe, 5/8/1995]
  If ABCD is a convex quadrilateral and M, N, P, Q are points on AB, BC, CD, DA respectively, prove that...

• Crossing a Canyon [Bullock, 5/10/1995]
  Basically, we're trying to cross a canyon. From a point on one side, a rope stretches across and drops ten feet vertically...

• Setting Sun [Messina, 5/19/1995]
  A fellow Naval retiree and I have been discussing whether the sun appears to set faster at the horizon near the equator than it does in the northern latitudes...

• Point reflected in a plane [DOG, 6/7/1995]
  How do I find the coordinates of point p' which is the reflection of point p in the plane E?

• Sin 20 and Transcendental Numbers [Wilkes, 6/29/1995]
  What is the significance of sin 20 in geometry?

• Dimensions of Rectangle [Arsenea, 7/10/1995]
  What are the dimensions of a rectangle if the area is equal to the perimeter?

• Minimum Distance from a Point to a Line [Salaz, 7/10/1995]
  Find all the values of b such that the minimum distance from the point (2,0) to the line y = 4/3x+b is 5.

• Trapezoid Median [Mascord, 8/14/1995]
  PQRS is a trapezium with PQ parallel to SR. If A and B are mid-points of SP and RQ respectively prove that...

• Surface Area of a Right Circular Cone [Klein, 9/5/1995]
  Could you please tell me the formula for finding the surface area of a right circular cone?

• Finding the Center of the Research Triangle [John, 9/5/1995]
  We live in an area known as the Research Triangle, with the triangle's points at the University of North Carolina, North Carolina State University and Duke University. We are interested in finding the center point of our triangle home and whether there is a unique term (or several terms) for the center point of a triangle.

• Intersections of Bisectors [Al, 9/6/1995]
  Explain how to get the incenter, circumcenter, and orthocenter of a triangle.

• Resources on 3D Surface Plots [Uygur, 9/12/1995]
  I would appreciate it if you would let me know of any databases or handbooks on the Internet for 3D surface plots of equations z=f(x,y,...).

• Surface Area of Solid Figures [Day, 9/18/1995]
  HELP!! My math teacher was talking today about the surface area of figures. I know about the area and how to find it, but I am confused about this.

• Hyperspace and the 4th Dimension [Buhler, 9/20/1995]
  May we have a general definition of hyperspace?

• Right Triangles [Kablay, 9/22/1995]
  How do you figure the angle of a right triangle when you only have the height and width?

• Calculating the Diameter of a Carpet Roll [Filip, 9/24/1995]
  How do you calculate the diameter of a carpet roll when you have the length and the thickness?

• Surface Area of a Cylinder [Cobb, 9/25/1995]
  What is the formula to calculate the surface of a cylinder with 25cm diameter and 20cm height?

• Software for Displaying Geometric Shapes [Corryn, 9/29/1995]
  Do you know where I could find a geometry program that would display geometric shapes?

• Resource for Euclidean and Non- Euclidean Geometries [Arun, 9/30/1995]
  For my high school project, I would like to get some information on Non-Euclidean geometry.

• Information on non-Euclidean Geometry [Melissa, 10/8/1995]
  A student asks for information on non-Euclidean geometry for a class project.

• Books about Proofs [Bandy, 10/26/1995]
  A student asks for help with geometry proofs, and Dr. Math suggests two books.

• Finding an Angle between a Line and a Line Segment [Gvl, 10/29/1995]
  What is the best way to find the angle between a line and a line segment that both originate at the same point?

• A Regular Nonagon [Hottes, 11/2/1995]
  I want to know if there is such a thing as a regular nonagon, and if not, why can't you get one?

• KaleidoTile [Bau, 11/15/1995]
  I would appreciate it if you would tell me a bit about KaleidoTile.

• Area of a Pentagonal Pyramid [Hayes, 11/16/1995]
  I would like to know the area of a pentagonal pyramid. The dimensions of the sides of the base are 5cm ea. and the height is 23cm.

• A Rectangular Prism [Jabber, 11/26/1995]
  Is it possible to have a rectangular prism that has a volume greater than its surface area?

• Area of Intersection of Two Circles [Jack, 12/1/1995]
  My teenage son asked me for the formula for the area of intersection of two arbitrary circles.

• Stellated Dodecahedron [Sccinc, 12/3/1995]
  A student asks for help finding information on stellated dodecahedrons.

• Who uses Ellipses? [Fu, 12/3/1995]
  I need to find out someone (or some occupation) that uses ellipses in their work.

• Proving the Pythagorean Theorem [Vogler, 12/5/1995]
  A friend of mine is irked because of constant use of the Pythagorean theorem, which he has not seen proven.

• Proving the Diagonals of a Rectangle Congruent [Zeke, 12/6/1995]
  How would you prove that the diagonals of a rectangle are congruent?

• Geometry Ladder Problem [Marley, 12/9/1995]
  A figure shows a 12-foot ladder leaning across a 5-foot fence and touching a higher wall located 3ft behind the fence. You want to find the distance x from the base of the ladder to the bottom of the fence. . .

• The Area of Triangles using Hero's Formula [Barber, 12/13/1995]
  If a person gave three dimensions of a triangle (in feet) and noted the base dimension, without knowing the angles because the other two lines would have to intersect someplace, is there a formula that could calculate the area?

• Isoperimetric Inequalities [Zielina, 12/16/1995]
  How can I prove that a circle has more area inside given its border length than any other shape?

• The Area of a Square Inscribed in a Circle [Thomas, 12/23/1995]
  What is the area of a square inscribed in a circle whose circumference is 16 (pi).

• Taxicab Geometry [Cazzato, 1/11/1996]
  I am looking for information online and/or in a college library about taxicab geometry.

• Finding the Area of an Arc [Ruffino, 1/23/1996]
  When you draw a circle and make a chord from one point to another, how would you find the area of that arc (formula)?

• Proving the Pythagorean Theorem in Two Steps [Vogler, 1/28/1996]
  I was trying to prove the Pythagorean theorem for a friend of mine, and eventually we figured it out. But then he said that he had heard of a "proof in only six easy steps." Do you know anything of this?

• Finding a Parabola [Blurch, 2/5/1996]
  Find the equation of the parabola that is one unit away from X^2 at all points.

• Incribing a Pentagon in a Circle [Evan, 2/6/1996]
  I'm stuck trying to inscribe a pentagon. I can easily inscribe a square by just drawing to pependicular diagonals. I also know that 360/5 = 72 but that doesn't help me at all. Can you help?

• Measuring Angles Using Steradians [Scaffidi, 2/8/1996]
  How do you measure a solid angle by using steradians?

• Isosceles Triangles [Risenhoover, 2/8/1996]
  A student asks how to find angle B of a given isosceles triangle.

• Calculating the Area of a Hexagon [Black, 2/10/1996]
  I've been trying to find a simple way to calculate the area of a hexagon given only it's width between two parallel sides.

• Ellipses: Pythagorean Relationship [Brett, 2/12/1996]
  In an ellipse with major axis of 2a, minor axis of 2b, and foci c (on the major axis), the relationship c squared = a squared - b squared holds true... how do the three numbers fit into a Pythagorean relationship?

• Geometry Proof - The Inscribed Angle is 1/2 of the Central Angle [Daniel, 2/12/1996]
  The grade 9 math book says the inscribed angle is 1/2 the central angle. Where can I find a proof, or can you offer a hint?

• How much does a Beam Bulge when it Expands? [Firebaugh, 2/24/1996]
  Imagine a railroad beam 1/4 mile long fastened at both ends. The beam expands 2" one summer day, causing it to bulge up. How high does it go?

• A Hexagon Inscribed within a Circle [Huang, 2/29/1996]
  A hexagon is inscribed within a circle. Three consecutive sides have a length of 3 and the other three consecutive sides have a length of 5. A chord is drawn within the circle....

• A Sphere in a Cube [Hoblit, 3/23/1996]
  I have a cube of 200x200x200 and a sphere with a radius of 100 is inside it. I want to be able to put in x and y and using a formula get z.

• Volume of a Rectangular Solid [Viola, 4/4/1996]
  How do you calculate the lateral area, total area, and volume of a rectangular solid with the following dimensions...

• Geometric Probability [Topp, 5/1/1996]
  What's the probability of an asteroid hitting the earth?

• Find the Length of a Carpet [Isberg, 5/3/1996]
  A carpet is placed diagonally in a rectangular room...

• trigonometry + geometry [kehatraj, 5/5/1996]
  A right angle triangle is blocking a circle and is being blocked by another circle...

• Midpoint of a Straight Line Segment [Williams, 5/7/1996]
  What is the midpoint of this: (-3,4) (5,-4)? Use the distance formula.

• Volume of a Cone [Laughnan, 5/9/1996]
  How much coffee can a tapered coffee pot hold?

• Pythagorean Theorem, Fermat's Last Theorem [Bluestein, 5/16/1996]
  Can the Pythagorean theorem be done with 3 different numbers?

• Circumference of an Ellipse [Pease, 5/18/1996]
  Is there a formula for determining the circumference or distance around an ellipse?

• Stewart's Theorem [Sonsino, 5/18/1996]
  I have to give a lesson/report on the history and uses of Stewart's Theorem...

• Picture Frame, Triangle Dimensions [Coleco, 5/20/1996]
  My teacher gave us ten questions to answer and I could do all except two: 1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base of a triangle is 9cm more than the perpendicular height...

• The Königsberg Bridge [Song, 5/20/1996]
  Do you have information on Konigsberg's bridge?

• Volume of a Pyramid [Tim, 5/20/1996]
  All six edges of a triangular pyramid are 4 inches long. Find the volume of the pyramid.

• Determining Distance Using Longitude and Latitude [Atlas, 5/21/1996]
  Use longitude and latitude to determine distance in rectangular coordinates.

• Can a Circle be a Polygon? [Smith, 5/22/1996]
  Could a circle be considered a polygon with an infinite number of sides?

• Trignometry [Pzgh, 5/24/1996]
  Why is the tangent of 90 degrees undefined?

• Moebius Strip [Brown, 5/24/1996]
  What would happen if you cut a moebius strip in half lengthwise?

• Polyhedron inside Sphere [Keays, 5/24/1996]
  How long do the sides of a dodecahedron have to be to fit into a sphere of diameter 2.9 m?

• Two-column Proof [Bond, 5/24/1996]
  Theorem: tangent segments from a point outside a circle to a circle have equal lengths.

• Formula for Common Tangents [Ristau, 5/27/1996]
  What's a simple formula that will define the common tangent of two circles of different diameters?

• Find angle DEB [sw4569, 5/27/1996]
  Given an isosceles triangle ABC...

• Finding a Point on a Circle [Gray, 5/28/1996]
  How do I find the y1 value?

• Finding the Center of a Circle [Java, 5/29/1996]
  How can you find the center of a circle using a ruler and compass?

• Derivation of Geometric Formulas [Swimduck, 5/29/1996]
  What are the formulas for the surface area, total surface area, and volume of a sphere, and volume of a pyramid and cone?

• Determine if Point is in Rectangle [Scott, 5/29/1996]
  What formula will allow me to determine whether a specified point lies within a polygon (rectangle - 4 points)?

• Archimedes' Method of Estimating Pi [Corinna, 5/29/1996]
  What was Archimedes' method for estimating pi using inscribed and circumscribed polygons about a circle?

• Geometry of a Pizza! [Lozowski, 5/31/1996]
  How can you divide a slice in half by cutting across a wedge?

• Area and Perimeter: Mowing the Lawn [ND3, 6/1/1996]
  How many circuits are necessary to cut half the lawn?

• Area of an unspecified triangle [Medalves, 6/1/1996]
  A square ABCD, with side "y", and an equilateral triangle DEF, with the same side "y", are in contact at point "d"...

• Area of a Triangle [Medalves, 6/2/1996]
  Knowing one side measures 1 and two adjacent angles measure a and b...

• Triangle Geometry: Sides and Edges [Dipak Naran Vallabh, 6/2/1996]
  If the angles of a triangle are equal, does it necessarily mean that the sides are also equal?

• Finding side lengths of a scalene triangle [medalves, 6/2/1996]
  Two observers on points A and B of a national park see a beginning fire on point C. Knowing that the angles CAB = 45 degrees, ABC = 105 degrees and that the distance between points A and B is of 15 kilometers, determine the distances between B and C, and between A and C.

• Logarithms and the Area of a Triangle [Alves, 6/3/1996]
  Is is true that if A is the area of a triangle, then....log(A) = ...?

• Painting Bell Towers [Kellar, 6/3/1996]
  I need to know the total surface area of three domes with assorted radii.

• Area, Volume of a Cone [Jenkins, 6/4/1996]
  What are the formulae to find the volume and area of a cone?

• Area and Volume of a Pear [Biener, 6/4/1996]
  How do you find the area and volume of a pear??

• Volume of Liquid in a Cylinder [Billman, 6/4/1996]
  How can I calculate the area under a chord of a circle - the amount of liquid in a cylinder laid in the horizontal plane?

• Circle Geometry [Jordan, 6/4/1996]
  Two circles intersect at A and N. One of their common tangents has points of contact P and T. Prove that <PAT and <PNT are supplementary.

• Strange Points of Locus [stse, 6/6/1996]
  Given two fixed points, A and B, on a plane, if P is a moving point such that PA and PB are perpendicular and the locus of P is a circle, should we exclude points A and B?

• Distance Calculation [Preller, 6/8/1996]
  If I have the co-ordinates of two places in Degrees Latitude and Longitude, how do I calculate the distance in nautical miles?

• Area of Union of Two Circles [Craig West, 6/10/1996]
  If the effective length of a rope tied to a goat is L, and the goat can eat exactly half of the grass in a field, express L in terms of R.

• Is Henry Guilty? (Geometry Puzzle) [Stevens, 6/10/1996]
  In Hughmoar County, residents shall be allowed to build a straight road between two homes as long as the new road is not perpendicular to any existing county road...

• Two Triangle Problems [Michael, 6/11/1996]
  One angle of a triangle is trisected... Find the shortest side.

• Apothem of a hexagon [m0812724, 6/11/1996]
  What is the forumula for the apothem of a regular hexagon?

• Area of a Rectangle Outside a Rectangle [Lambert, 6/11/1996]
  Find the area of the concrete border of a rectangular swimming pool.

• Coordinates of a Point [Wong, 6/12/1996]
  ABC is a right-angled triangle labeled counter-clockwise with its point C lying on the line y=3x. A is (2,1) and B is (5,5). Find the two possible coordinates of C.

• Inscribed Angle, Circle Equation [Arthur, 6/14/1996]
  What's an inscribed angle? What's the equation for a circle with a center at (8,-1) and a radius of 15?

• Cosines and Sines [Boschem, 6/16/1996]
  Why does cos A = sin (90 - A)?

• Stella Octangula [Math2, 6/17/1996]
  What is the name of the polyhedron that looks like the union of two tetrahedrons joined at their bases?

• Distance Between Two Points on the Earth [Coopersmith, 6/21/1996]
  My latitude and longitude are in the form 40.266934, -74.204930 respectively, with negatives for South and West. How do I calculate the distance between them?

• Length of Material on a Cylindrical Roll [d14now, 6/21/1996]
  Is there a formula for calculating the length of material on a roll knowing the roll diameter, the core diameter, and the material thickness?

• Isosceles Trapezoid [Brady, 6/23/1996]
  Bases AB and CD of an isosceles trapezoid ABCD are 12 units apart...

• Euclid's Fifth Postulate [Minsley, 6/24/1996]
  I am interested in finding some theorems, axioms, or postulates similar to Euclid's Fifth Postulate.

• Mapping Points [Trigonix, 6/25/1996]
  How do you map points inside a 4-point convex polygon onto another 4 point convex polygon?

• Congruent Triangles [Lewis, 6/26/1996]
  If two triangles have the same area and the same perimeter, must they be congruent?

• Circumference of an Ellipse [Reese, 6/27/1996]
  What is the formula for the circumference of an ellipse?

• Bounding Rectangle for an Ellipse [CarlGroup, 6/28/1996]
  I would like to know if there is a general equation for a bounding rectangle of an ellipse.

• If You Know Perimeter, Can You Find Area? [Thompson, 6/30/1996]
  Can one determine the acreage of an irregularly shaped field if only the distance around the edge of the field (in feet) is known?

• Formula for the Surface of a Cylinder [Macrobie, 7/2/1996]
  What is the general formula for the surface of a cylinder?

• Formula for the Length of a Chord [Kjellin, 7/3/1996]
  What is the formula for the length of a chord given either the circle radius or the area of the resulting circle segment?

• Product of the radii [Gerard, 7/3/1996]
  The length of a common internal tangent to two circles is 7, and a common external tangent is 11...

• Two Discs, One Rotating [Leung, 7/5/1996]
  Two circular discs have radii 8 cm and 28 cm. The larger disc is fixed while the smaller disc rolls around the outside of the larger...

• Circle in n Sectors [Siong, 7/8/1996]
  A circle is completely divided into n sectors in such a way that the angles of the sectors are in arithmetic progression...

• Side Lengths of Isosceles Triangle [Dave, 7/8/1996]
  Given two isosceles triangles on top of one another... find the unknown side lengths.

• Triangle and Circle with same Center [Geldermann, 7/8/1996]
  An equilateral triangle and a circle have the same center... find the length of the side of the triangle.

• Volume of Cube, Tent [Zimmer, 7/9/1996]
  How do I calculate the volume of a cube and a tent... and the capacity of a cylinder and a tent?

• Area of a Hexagon [Denofsky, 7/9/1996]
  How do you calculate the area of a hexagon?

• Ellipse Bounding A Rectangle [Carl, 7/15/1996]
  How do I calculate the ellipse bounding any given rectangle?

• Number of Points in a Star [Saxon, 7/16/1996]
  Is there a way to predict the number of points in a star given only the internal angle of the corners?

• Cone Symmetry [Kang, 7/17/1996]
  Why does a circular cone have infinite lines of symmetry?

• Ratio of Areas of Triangle and Parallelogram [Gerard, 7/17/1996]
  Given a parallelogram in a triangle... compute the area of the triangle divided by the area of the parallelogram.

• Angle Between Two Points on the Globe [Shelton, 7/17/1996]
  Given their longitude and latitude, how can you determine the angle in radians between two cities?

• Product of Radii of Two Circles [Darwent, 7/22/1996]
  The length of a common internal tangent to two circles is 7, and a common external tangent is 11...

• Volume of Irregular Pyramid of Human Arm [Bakhtiary, 7/24/1996]
  I form an irregular pyramid from my arm, forearm, shoulder and wrist in the rest position (forearm rested on a table). Is there any way to measure the volume of this irregular pyramid?

• Area, Angle of Chords of a Circle [Siong, 7/25/1996]
  Calculate the angles PAB and POB, the area of the sector bounded by OP, OB and the minor arc PB.

• The Diameter of an Octagon [Michael, 7/25/1996]
  What is the diameter of an octagon with each side length equal to 2 inches?

• Use of Steradians [Skaffml, 7/26/1996]
  How are steradians used in real life?

• Area, Circumference of an Ellipse [Kroon, 7/29/1996]
  How do I calculate the area and circumference of a given ellipse?

• Obtuse and Oblique [Hackett, 7/29/1996]
  Are the terms "obtuse" and "oblique" interchangeable?

• Picture of Icosahedron [Sobotka, 7/31/1996]
  Do you have a picture of an icosahedron?

• Prove Triangle of Sides with Length... [Chen, 8/1/1996]
  Let a, b and c be the lengths of the sides of a triangle. Prove that the square root of (a+b-c) plus the square root of (b+c-a) plus the square root of (c+a-b) is equal to or less than the sum of the square roots of a, b and c. Determine when equality occurs.

• Area of an Irregular Polygon Given Side Length [Paul, 8/2/1996]
  What is the area of an irregular quadrilateral with side lengths in a clockwise order of 43.61, 133.64, 146.96, and 110.85?

• Names of Parts of a Cone [Bonnie, 8/2/1996]
  Are the components of a net of a cone called faces in all cases, or only for polyhedra?

• Volume of a Triangular Tank [Daubner, 8/5/1996]
  What's the volume of a triangular tank 3'4"x3'4"x5' and 22" in height?

• Goat on a Rope [Nicholls, 8/6/1996]
  A circular field has a fence around its edge; how long does a rope need to be so that a goat can graze exactly half the field?

• Water in a Horizontal Tank [Michael, 8/7/1996]
  What's the volume of water in a cylindrical tank 72" long and 36" in diameter, filled only to 4.25"?

• Integral of Triangular Surface [Suresh, 8/9/1996]
  Is it possible to numerically integrate S { 1/3 (x^3 i + y^3 j + 0 k) . n} dS where n is the unit normal to the surface S, a triangle in a plane?

• Express y-Coordinate of Point... [plkhoo, 8/9/1996]
  P and Q are the points of intersection of the line y/2+x/3 = 1 with the x- and y- axes respectively. The gradient of QR is 1/2 and R is the point whose x-coordinate is 2t, where t is positive....

• Sphere Eversion [Jenkins, 8/11/1996]
  How do you mathematically turn a sphere inside out?

• Finding a Point Equidistant From Two Other Points [Jason, 8/18/1996]
  Point A is (-5,-3), and point B is (-1,-5); to be equidistant from A and B, what should the value of k be for the point (3,k)?

• Distance Between 2 Lines: Vectors [Wolfe, 8/19/1996]
  What is the shortest distance between 2 lines?

• Polygon Diagonal Formula [Myer, 8/20/1996]
  Does the polygon diagonal formula apply to other parts of geometry?

• Geometric Interpretation of Inequality [Horrocks, 8/23/1996]
  If z1 and z2 are complex numbers, interpret geometrically the inequality | z1 + z2 | < | z1 | + | z2 |.

• Quadrilateral Area Given Side Lengths [Robinson, 8/24/1996]
  I need to find the area of a 4-sided figure, given its side lengths.

• Pythagorean Triple [Patrick, 8/28/1996]
  What is the formula for finding the three lengths in a Pythagorean triple where the shortest side is even?

• Radius, Center of Circle Given 3 Points [Simmons, 8/28/1996]
  What is an easy formula to calculate the center point and radius of a circle given three points on the circumference?

• Cyclic Quadrilaterals [Digby, 8/30/1996]
  A cyclic quadrilateral touches a circle at each vertex. What angles do these points make with the centre of the circle?

• Surface Area of Earth (a Sphere) [Melanie, 8/30/1996]
  Could you tell me the formula for determining the surface area of a sphere?

• Cylinder of Arbitrary Axis [Vallis, 9/2/1996]
  What is the equation of a cylinder about an arbitrary axis...?

• Angle, Side Length of a Triangle [Inman, 9/4/1996]
  What is the relation between the angles and side lengths of a triangle?

• Pick's Theorem [Jeff, 9/4/1996]
  Could you explain Pick's Theorem?

• The Perimeter of an Ellipse or Oval [Friend, 9/5/1996]
  What is the formula for calculating the perimeter of an oval, or an ellipse?

• Sum of Two Vectors [Kruger, 9/10/1996]
  Why is the magnitude of the sum of two vectors less than or equal to the sum of the magnitudes of each vector?

• Circumference of a Circle Given Chord Length [Kloof, 9/11/1996]
  Given the length of a chord of a circle, is it possible to determine the circumference?

• Circular Field, Cow, and Length of Rope [Bnby57, 9/11/1996]
  A cow is tied with a rope to the edge of a circular field 10 ft. in diameter. How long must the rope be so the cow can graze half the field?

• Broken Flag Pole [Lightfoot, 9/11/1996]
  A 90 ft high flag pole sits atop and in the corner of a 10 ft high, 10 ft wide building. The pole breaks...

• Sum of Angles of Polygon... [Thompson, 9/24/1996]
  Assuming the equality of alternate interior angles formed by a transversal cutting a pair of parallel lines, prove...

• Square with same Perimeter and Area as a Triangle [Edwards, 10/16/1996]
  I've been hunting for a square/triangle combination with the same perimeters and areas. Is this possible?

• Line with Small Compass and Straightedge [Hills, 10/16/1996]
  Construct a line segment joining two points farther apart than either a compass or the straightedge can span.

• Direction of Travel [Hynes, 10/18/1996]
  If I know the latitudes and longitudes of where I am coming from and where I want to go, how do I figure out what compass heading to follow?

• Tangent to Parabola [Spoelhof, 10/21/1996]
  What is the slope of the lines tangent to the parabola y = x^2 that pass through the point (2,1)?

• Interior Angles of a Polygon [Rhodes, 10/21/1996]
  The sum of the measures of the interior angles of any convex polygon with n sides is (n-2)180 degrees. Does this theorem apply to concave polygons?

• Dividing Regular Shapes [Moss, 10/22/1996]
  If every vertex of a triangle is joined by straight lines to 6 points on the opposite side of the triangle, how many regions are formed? If every vertex of a regular pentagon is connected to every other vertex, how many triangles are formed?

• Lines Intersecting within a Polygon [Loveland, 10/24/1996]
  Given an n-sided regular polygon with all vertices connected to each other by straight line segments, how do you determine the number of intersection points within the polygon?

• Knot Theory [Sen-Gupta, 10/24/1996]
  What does Knot Theory actually describe and mean, what does it state about knots, and what is its usefulness in real life?

• Spherical Triangles [Knoop, 10/26/1996]
  Why can't you use the Pythagorean formula to measure the distance between two points on Earth?

• Finding the Radius of a Sphere [Harper, 10/28/1996]
  Can you find the radius of a sphere if you don't know the volume or surface area?

• Polyhedron Problem [English, 10/29/1996]
  How many faces share each edge?

• Tetrahedron Projected on a Plane [English, 10/29/1996]
  How do you project a regular tetrahedron perpendicularly onto a plane to get the maximum area shadow?

• Bouncing Cue Ball [Nichole, 10/29/1996]
  A cue ball is launched at an angle of 45 degrees from the lower left corner of a pool table and ends up in the lower right corner. What rule will predict which corner the ball will hit? What patterns are involved?

• Descartes' Square Root Method [Potivn, 10/30/1996]
  Why does Rene Decartes' geometric method for finding square roots work?

• Formula for Factors of a Number [Daniel, 11/3/1996]
  How many triangles can you draw on a square grid of dots of size x*x?

• Combinations of Cubes [Whistler, 11/07/1996]
  How many different cuboids can be made from one million connectable cubes, using all the cubes?

• Triangles within a Triangle [Jensen, 11/10/1996]
  If multiple small equilateral triangles are drawn within a larger one, what is the relation between the number of small triangles lying on the base of the big triangle and the total number contained within the big triangle?

• A Coordinate Geometry Problem [Lud, 11/26/1996]
  Given two perpendicular lines AC and BD in a plane and a point E directly above their intersection, find the length of BC.

• Area of an Unusual Hexagon [Fletcher, 12/05/1996]
  Find the area of a hexagon made from a triangle with squares appended to each of its sides and three more triangles each consisting of one unknown side and two sides which are shared with two of the squares.

• Using Relative Primes [Chin, 12/07/1996]
  Given a floor 105 tiles wide and 135 tiles long, how many tiles will a diagonal drawn from one corner to the opposite corner intersect?

• Trisecting an Angle [Chadwell, 12/16/1996]
  An explanation of how to trisect a 90 degree angle, plus some constructions.

• Parametrics [Neil, 12/18/1996]
  You're in 3-D space at point A, you want to get to point B, and you know the coordinates to point B from point C (but B is moving). What heading do you need to set in order to meet point B?

• Finding the Center of a Circle [Heikke, 12/26/1996]
  Given a circle of radius R with center point unknown, a line with equation Y = mx+b and a line at Y = -.08, find the x,y coordinates of the points of tangency where the two lines intersect the circle.

• Hole in a Sphere [Klein, 12/30/1996]
  When you bore a 6 inch cylindrical hole through the center of a sphere, what is the volume of the remaining solid?

• Triangle Centroid in 3-Space [Chute, 12/30/1996]
  Given three points in 3-space that, when connected, form a triangle, what are the coordinates of the centroid?

• Finding Coordinates [Rounceville, 12/31/1996]
  Given two intersecting line segments, the angle they form at their intersection, the coordinates of one endpoint and those of the intersection, and the length of one of the line segments, how do you determine the coordinates of the remaining endpoint?

• Platonic Solids [Rodalbough, 01/01/1997]
  Is there such a thing as a regular 7-hedron?

• Projective Geometry [Andrew, 01/13/1997]
  When seen from a semi-bird's eye view, a fractal terrain looks like a regular trapezoid. When rotated right or left, the four corners seem to move along an ellipse. Find the equation of the ellipse whose center is also that of the trapezoid.

• Definition of a Trapezoid [Cunningham, 01/15/1997]
  What is the correct definition of a trapezoid, and why?

• Using the Cartesian Plane [Steve, 01/19/1997]
  Draw a rectangle that is Sqrt(2) by 1 with corners at (0,0), (1,0), (1,Sqrt(2)), and (0,Sqrt(2)).

• Angle of Elevation [David, 01/22/1997]
  A tree 66 meters high casts a 44-meter shadow. Find the angle of elevation of the sun.

• Symmetry in Platonic Solids [Thompson, 01/24/1997]
  How many planes of symmetry does each of the platonic solids have?

• Finding the Center of a Circle [McClung, 01/24/1997]
  Given two points on a circle and the circle's radius, find the center coordinates of the circle. HS Algebra, Geometry Rachel

• Earth's Curvature [Choksi, 01/27/1997]
  How do you figure out the degree of curvature of the earth's surface?

• Polygon Angles [Colschol, 02/14/1997]
  What is the sum of the measure of the angles in polygons with sides 3-50?

• Why So Much Math? [Forhand, 02/24/1997]
  How is geometry ever going to help me in my career as a police officer?

• Math and Sports [Parrish, 02/26/1997]
  Can you give me information on how math relates to sports?

• Quadrilateral Patterns [McDonel, 03/06/1997]
  What is the formula that gives the number of quadrilaterals within a square grid when you increase the square grid by one unit on each side?

• Finding Polygon Areas [Worden, 03/20/1997]
  How do I find the area of polygons?

• Formulas: Width, Side Length of Octagon [Perkins, 03/24/1997]
  Given the width of an octagon, what is the length of a side, and vice- versa?

• Sphere Formulas [Rhoades, 03/26/1997]
  What are the formulas for area and volume of a sphere?

• Perimeter of Octagon [Rodano, 04/02/1997]
  What is the perimeter of a an octagonal garden with a diameter of six feet?

• Polygons and Circles [Solomon, 04/03/1997]
  Why is it that a regular polygon with an infinite number of sides is a circle?

• Impossible Constructions? [Steffenson, 04/08/1997]
  My geometry teacher told us there are 3 impossible problems or constructions - what are they?

• Right Angle [Verma, 04/09/1997]
  In a rectangle, draw a line from one vertex to a side to an adjacent vertex. Determine what makes the angle formed in this process 90 degrees.

• Theta [Allen, 04/14/1997]
  What is Theta? Does it have a constant value?

• Pythagorean Triples [Paulsen, 04/14/1997]
  Why can't all the numbers in a Pythagorean triple be prime?

• Circle and Polygons: Lines of Symmetry [Rynodunk, 04/14/1997]
  How many lines of symmetry are there in a circle?

• Constructing an Ellipse [Brantley, 04/15/1997]
  How do you draw an ellipse?

• Coordinate Systems [Eagle, 04/22/1997]
  What is the polar coordinate system and how does it differ from the rectangular coordinate system?

• Area of a Trapezoid [Browne, 04/27/1997]
  Find the area of a trapezoid with three sides of length 80 and one of length 120.

• Point in a Circle [Zolnierz, 04/29/1997]
  Given a circle with two 6-inch chords running across the top and the bottom... find the probability that a point chosen at random is in the region between the chords.

• Topology [Gray, 05/10/1997]
  What is topology? What is knot theory?

• Point on an Ellipse [Kadel, 05/16/1997]
  Given an ellipse and an arbitrary angle theta from either axis, how do you find the coordinates of the intersection of the ellipse and a vector formed by angle theta?

• Distance from Point to Ellipse [Ingrum, 05/19/1997]
  How do you find the minimum distance from a point to an ellipse when the point can be either inside or outside the ellipse?

• Interior Angles of a Polygon [Deitz, 05/20/1997]
  How do you figure out the sum of the interior angles of a polygon?

• Diagonals of Polygons [Kelly, 05/21/1997]
  How many diagonals does a polygon with n sides have?

• Volume of ellipsoid [Chung, 05/22/1997]
  I have forgotten how to calculate the volume of ellipse.

• Pick's Formula [Lee, 05/22/1997]
  What is Pick's Formula?

• The Goat In the Field Problem [Miller, 05/24/1997]
  A farmer tethers a goat to the circumference of a circular field. What ratio of field radius to length of rope must he use so that the goat can graze only half the area?

• Spherical vs. Plane Geometry [Tsang, 05/30/1997]
  How is spherical geometry different from plane geometry?

• Tessellations and Symmetries [Fang, 06/07/1997]
  How do you make a tessellation with a rotation, reflection, and translation all in one shape?

• Nine-Sided Polygon [Semenoff, 06/11/1997]
  Can you construct a regular 9-sided polygon inside a circle using only a compass and straight-edge?

• Point on a Plane [Schnell, 06/13/1997]
  If I know the coordinates of three points that form a plane and the first two coordinates of another point on that plane, how do I find the third coordinate of that point?

• Mars '98 Lander [Brill, 06/18/1997]
  Given an arbitrary quadralateral in which all interior angles and two opposite sides are known, how do you find the other sides?

• Drawing Triangles [Joe, 06/18/1997]
  Is it possible to draw a triangle with more than 180 degrees?

• Coordinates of Right Triangles [Wade, 06/25/1997]
  Find all possible values of k so that (-1,2), (-10,5), and (-4,k) are the vertices of a right triangle.

• Area of a Polygon [Wilhelm, 06/27/1997]
  If you know the coordinates of the vertices, how do you calculate the area of a polygon?

• Finite vs. Infinite [Angie, 07/10/1997]
  If a line segment is a measurable part of a line, why is the number of points that make up a line segment infinite?

• Pythagorean Triples [Toscano, 07/14/1997]
  Is there a formula to determine the solutions to the following equations? a^2 + b^2 = c^2, a^3 + b^3 + c^3 = d^3...

• Geometry Unit on Quilting [Kouloufakos, 07/16/1997]
  Do you have any information/units/lessons/curriculum ideas on quilting in mathematics?

• Triangle Perimeter [Caraher, 07/20/1997]
  How many triangles have sides whose lengths total 15 units?

• Finding the Arc Length of a Hanging Catenary [Kd38, 07/23/1997]
  A catenary is suspended between two equal poles 400 feet apart at equal height; it sags in the center 40 feet...

• Right Angles in Polygons [Lok, 07/23/1997]
  Is there a relation between the number of sides in a polygon and the maximum number of right angles?

• Distance to Mars [Gonzalez, 07/25/1997]
  What is the distance from Earth to Mars?

• Area of a Curved Figure [Hamby, 07/26/1997]
  How can you find the area of a curved figure without using calculus?

• Surface Area of an n-dimensional Sphere [Bollinger, 07/28/1997]
  I was wondering how to calculate the surface area of a sphere in n dimensions.

• Determining Distance between Two Cities [Remen, 07/30/1997]
  I need an equation to use in an application for a car dealership.

• Octagon Formula [Ecker, 07/30/1997]
  If you're building an octagon on a 12-foot radius, what is the length of each side?

• Miter for a Pyramid [Champion, 07/31/1997]
  I want to construct a 4-sided pyramid out of glass for a garden fountain. I need to know the degree of miter to put on the edges of the uprights of the triangles...

• Complex Ratio Problem [JDJ, 07/31/1997]
  If you randomly throw 3 points on a plane, you get a triangle... What is the probablilty that the triangle will become obtuse...?

• Container Height and Volume [Hemingway, 08/01/1997]
  A container's height is increased by 4 cm, and the length and width remain the same. If this change increased the volume by 12 percent, what was the original height of the container?

• Finding Distance Using the Earth's Grid System [Grand, 08/05/1997]
  How do I find the shortest distance between two points on the earth using degrees of latitude and longitude?

• Geometrically Completing the Square [Brennan, 08/07/1997]
  What are the steps for geometrically completing the square?

• Donkey Grazing Half a Field [Steele, 08/08/1997]
  A donkey is attached by a rope to a point on the perimeter of a circular field. How long should the rope be so that the donkey can graze exactly half the field?

• Euler's Formula for Polyhedra [Knobler, 08/12/1997]
  How would you prove Euler's formula V-E+F = 2 for all polyhedra of genus zero?

• Volume of Inscribed Cylinder [Denton, 08/14/1997]
  A cylinder of height h is inscribed in a sphere of radius q. Find an expression for the volume of the cylinder.

• Ellipse [Gallo, 08/17/1997]
  How do you form an ellipse using 3 points?

• Angles of Stars [Aande, 08/18/1997]
  What are the interior and external angles of stars built on regular pentagons and octagons.

• Square Peg, Round Peg [Tony, 08/22/1997]
  Which fits better, a square peg in a round hole, or a round peg in a square hole?

• Research in Dynamic Geometry [Gravina, 08/27/1997]
  Is there research on overcoming difficulties in learning Geometry (transition to formal proofs) by using Dynamic Geometry environments?

• Research in dynamic geometry [Gravina, 08/27/1997]
  I would like to know about research into learning Geometry using Dynamic Geometry environments.

• Analytic Geometry [Olden, 08/31/1997]
  How do I find the standard equations of the circles that pass through (2,3) and are tangent to both the lines 3x - 4y = -1 and 4x + 3y = 7?

• Bearing Calculation [Vojnic, 09/01/1997]
  Given two cities at geographic coordinates (xA,yA) and (xB,yB), is there a formula to calculate the bearing from city A to city B?

• Finding Areas of Different Polygons [Alex, 09/02/1997]
  Could you please tell me how to work out the area for an equilateral heptagon, octagon, nonagon, decagon, unedecagon, and dodecagon?

• Depth of a Tank [Rossman, 09/04/1997]
  A tank 100' long and 10' wide holds 15,000 cu. ft. of water...

• Area of a Parabola [Globetrotters, 09/05/1997]
  How do you find the area of a parabola? (I just finished Algebra 2.)

• Volume of a Cylinder [Adams, 09/05/1997]
  How do you calculate the volume of a cylinder laid on its major axis if you know the heights of the top and bottom of the section?

• Ptolemy's Theorem [Breitling, 09/07/1997]
  Can you give me a reference for the proof for Ptolemy's Theorem?

• Proof of Hero's formula [Boyd, 09/08/1997]
  Could you tell me where to find a proof of Hero's formula or help on how to derive it?

• Equation for an Arch [Cashell, 09/09/1997]
  I am trying to draw an arch that will go in the ceiling of a building. The arch will be at a maximum height of 28 inches...

• Longitude Degrees at the Equator [Parrinello, 09/09/1997]
  What is the distance in miles between degrees of longitude at the equator?

• Cleaning the Ice [Jones, 09/09/1997]
  The hockey rink is a rectangle, 120 ft. by 60 ft. The scraper cleans a 4-ft.-wide strip... on which trip will it have cleaned half the area of the rink?

• Circle Inscribed in a Right Triangle [Hadden, 09/09/1997]
  What is the diameter of the circle if the legs of the triangle are known to be A and B?

• Solve for Radius [Culpepper, 09/09/1997]
  Given a circle through three points, what is the equation for the intersection of the perpendicular bisectors?

• Overlapping right triangle problem [Wilson, 09/14/1997]
  Given right triangles ABC and DCB with rt angles at B and C, triangle ABC's hypotenuse 20 and triangle DCB's hypotenuse 30. The hypotenuses intersect at point E, a distance of 10 from BC. Find the length of BC.

• Archimedes and the Area of a Circle [Calabrese, 09/17/1997]
  How do you find the area of a circle without pi?

• Distance to the Horizon [Turner, 09/18/1997]
  A 6-foot man is standing on the beach at sea level looking straight out to sea. How far can he see - i.e. what is the distance from the man to the horizon?

• Proof by Contradiction [Price, 09/25/1997]
  Prove that no isoceles right triangle exists which has all three sides integers.

• Square Inscribed in a Circle [Steve, 09/28/1997]
  What percent of the circle is contained within the square?

• Volume of Dirt [Budzynski, 09/29/1997]
  You have a mound of dirt that is 2 meters high with a bottom radius of 1 meter...

• Parallelogram Perimeter [Nutting, 10/01/1997]
  The diagonals of a parallelogram are 10 and 24 in length. If one side of the paralellogram is 13, what is the perimeter?

• Volume of a Solid [Rasmussen, 10/02/1997]
  The base of a solid is the region inside the circle x^2 + y^2 = 4...

• Surface Area of a Sphere [Kaszuba, 10/03/1997]
  How is the surface area of a sphere calculated, and why?

• Product of Isometries [Marie, 10/05/1997]
  Use three isometries (translation, rotation, and reflection) in composition with each other and deduce the net result of the two transformations.

• Chord Proofs [Burke, 10/07/1997]
  Prove that in any circle a radius perpendicular to a chord also bisects the chord... a radius that bisects the chord is perpendicular to the chord... chords equidistant from the center of the circle are congruent.

• Geometry of a Circle (Arcs and Angles) [Nieves, 10/13/1997]
  DE is a diameter of circle O, and is perpendicular to chord AB at point C...

• Angle-bisector Proof [Gelfand, 10/16/1997]
  Prove that in a triangle ABC, a pair of angle-bisectors cannot be perpendicular.

• Proving Pi and Buffon's Needle [Billings, 10/19/1997]
  What experiment can I do to prove pi using both mathmatics and science?

• Traceable Mathematical Curves [Heaps, 10/27/1997]
  Is there any way to tell just by looking if a curve is traceable or not? Is there some property of a curve that will tell you this? Do curves have formulas?

• Is it Possible to Prove that... [Coates, 10/28/1997]
  ... if the hypotenuse of a right angle triangle is divisible by 4, the legs are also divisible by 4?

• How much Material to Purchase? [Peterson, 11/01/1997]
  Sanchez warehouse wants to install a 3-foot wide ramp from the level floor to the top of the 4-foot high platform...

• Derivation of Law of Sines and Cosines [Yuan, 11/02/1997]
  How do you derive the law of sines and the law of cosines?

• Trisecting a Line [Federow, 11/03/1997]
  How would you trisect a line using a compass and a straight edge?

• Rotational Symmetry [Auge, 11/05/1997]
  I am looking for a precise definition of rotational symmetry of a figure in a two-dimensional plane.

• Optimization: Minimum Area [Yamashita, 11/07/1997]
  How do you fold a piece of paper (rect. with width a and unlimited length) so one corner just reaches the righthand side for minimum area?

• Volume and Pi [Lail, 11/10/1997]
  How do you find the volume of a cylinder that is 7.5mm high and has a diameter of 4mm?

• 3D Geometry [Fallon, 11/17/1997]
  You can draw a line of minimum distance between and perpendicular to two lines in 3space. I know how to get the distance and direction of this line, but I want to locate the line in 3space so that I can find its midpoint.

• Drawing An Ellipse [Liu, 11/24/1997]
  How do you draw an ellipse with only a straight edge and a compass?

• Limited Area, Unlimited Perimeter [Rosa, 11/27/1997]
  What is the figure?

• Area of an Ellipse [Vinay, 11/28/1997]
  How do you find the area of an oval without using calculus?

• Geometry of a Bicycle [Sara, 11/30/1997]
  How do you show everything geometrical about a bicycle?

• The Math Behind Music: Pitches, Scales, Geometry [Angelica, 12/03/1997]
  Connections between music, physics, and math.

• Point and Line Symmetry in the Alphabet [Montone, 12/05/1997]
  What letters of the alphabet have point symmetry, line symmetry, or both? How many have neither form of symmetry?

• Geometry - Parallel Lines [Kamenezky, 12/09/1997]
  Given: EJ = EK; JK||MN; Prove: Angle M = Angle N.

• Distance Between Points on the Earth [Hollingshead, 12/11/1997]
  The problem is to solve for the distance between two latitude/ longitude points with no parallels, say 24N 70E and 65N and 30W.

• Cosine Addition Formula [Memon, 12/13/1997]
  How can you prove the addition formula for cosine by using right triangles?

• Find a Function, Integrals [Lanka, 12/17/1997]
  Suppose the graph of f has the formula f(x)=-x+1 for 0<=x<=1; x-1 for 1
• The Shortest Crease [Shanger, 12/29/1997]
  A piece of paper is 6 units one side and 25 units on another side...

• Heron's Area Formula [Clemen, 12/30/1997]
  I need to write a proof of Heron's Area Formula.

• Topology [Bullard, 12/31/1997]
  Is there a simple definition for homeomorphism? for topology?

• Distance of Chord from Circumference [Simpson, 12/31/1997]
  Is it possible to calculate the vertical distance, at a right angle, from a chord to the circumference of a circle?

• Impossible Constructions [Coconut, 01/14/1998]
  What are the three ancient impossible construction problems of Euclidean geometry?

• Shortest Distance between Points [Justin, 01/17/1998]
  I am doing a project on the shortest distance between two points via another plane. I need help with my theorems.

• Cow Grazing Half the Circle: Newton-Raphson Method [Julus, 01/18/1998]
  Assume a perfect circle filled with grass and a cow tied with a rope to the fence around it...

• Proving the Pythagorean Theorem [Neusihin, 01/27/1998]
  Can you please explain how I can prove the Pythagorean theorem?

• Radius of a Sphere [Guerrero, 01/29/1998]
  What is the ratio of the areas and volumes of two spheres, one with radius 3 times the other? What possible theorems are suggested?

• Cycloid [Chris, 01/30/1998]
  What is a cycloid and what does it do?

• Volume of Spherical Cap [Arkin, 02/06/1998]
  I am trying to find the volume of a cap of a sphere with radius of 5. The cap has a height of 3 - it is as if the top of the sphere, 3 meters from the top, was severed from the rest of the sphere.

• Polyhedra: Classification, Theorem [Barnett, 02/12/1998]
  I would like to know how polyhedrons are classified, which figures can be used for the faces, and the theorem relating the faces, edges, and vertices.

• Pythagorean Theorem and Cubes [Shott, 02/14/1998]
  In a cube if a diagonal is drawn from the front top corner to the back bottom corner, how long must each side be using the Pythagorean Theorem?

• Intersection of Angle Bisectors of Triangles [Swaine, 02/17/1998]
  Prove that bisectors of each angle of a triangle intersect at one point.

• Areas of House Lots [Redfearn, 02/18/1998]
  We have to determine sanitary sewer assessments of properties based on the square feet of their lots. Many lots are 4-sided but do not have any parallel lines...

• Proof of Pythagorean Theorem [Hagedorn, 02/23/1998]
  I would like to know how Pythagoras reasoned his theorem.

• The Centroid of a Triangle [Jamry, 02/25/1998]
  WHY is the centroid of any triangle the center of its balance?

• Tessellation [Stacey, 02/26/1998]
  Are there any non-regular convex polygons with more than four sides that can tessellate?

• Area of A Sector of An Ellipse [Brady, 02/28/1998]
  Finding the area of a sector of an ellipse, given the semiminor and major axes and the angles of the 2 vectors bounding the sector.

• Limit of Area [Jason, 03/01/1998]
  Limit approached by area of a square when its sides are repeatedly divided into three congruent parts and squares are constructed outwardly on the middle parts.

• Formula for Area of Any Regular Polygon [Miklas, 03/01/1998]
  Area of a regular polygon, given the number of sides and length of a side.

• Three-dimensional Counterparts for Two-dimensional Objects [Amy, 03/04/1998]
  Three-dimensional counterparts for lines, polygons, perpendicular lines, and collinear lines.

• Degenerate Conics [Kiczek, 03/04/1998]
  Identifying the degenerate cases for the graphs of equations in conic form.

• Analytic Proof that Midpoints Form a Circle [Dunlavy, 03/10/1998]
  Analytic proof that midpoints between a point within a circle and its circumference form a circle.

• Trisecting Angles [Bran, 03/10/1998]
  An angle of 180/n, for n a positive integer not divisible by 3, can be trisected.

• Number of Lines of Symmetry in a Regular Polygon [Cook, 03/12/1998]
  In a regular polygon, is the number of lines of symmetry the same as the number of lines or angles of that polygon?

• Locus of the Midpoint of a Chord [Chew, 03/13/1998]
  Show that the locus of the midpoint of the chord is a hyperbola.

• Sides of a 30-60-90 Triangle [Totten, 03/13/1998]
  In a 30-60-90 triangle where the short side is X, why does the hypotenuse equal 2X and the long side equal X * sqrt(3)?

• Counting Diagonals [Thompson, 03/14/1998]
  How many diagonals can be drawn for a polygon with n sides?

• Proportions of Exact Enlargements [Emma, 03/18/1998]
  How are two objects related if one is an "exact enlargement of the other"?

• Triangle and Circumscribed Circle [Richardson, 03/23/1998]
  How can you find the radius of a circle circumscribed around any triangle given the three outside points of the triangle.

• Golden Spiral [Dobney, 03/23/1998]
  What is the equation of the Golden Spiral?

• Volume of a Cone or Pyramid [Swan, 03/30/1998]
  Proofs that the volume of a cone or pyramid is (1/3)b*h.

• Distance From a Point to a Plane [Larock, 03/31/1998]
  Can you show me the proof of the formula for the distance between a point and a plane?

• What Does "Stellated" Mean? [Origami Club, 03/31/1998]
  Stellating polyhedra, including solids that are already stellated.

• Diagonals and Axes of Symmetry [Dobing, 03/31/1998]
  Could you explain the concepts behind the diagonals and axes of symmetry in a regular octagon?

• Deriving the Law of Cosines [Lawrenson, 04/01/1998]
  Will the Pythagorean Theorem work with a non-right triangle?

• Explaining the Dot Product [Waycaster, 04/05/1998]
  Exactly what does the dot product represent?

• Impossibility of Constructing a Regular Nine-Sided Polygon [Su, 04/07/1998]
  Can you construct a regular 9 sided polygon with just a compass and straightedge?

• Trapezoid: Visual Proof of Area Formula [Dwight, 04/11/1998]
  How can I prove visually that the area of a trapezoid is half the sum of the parallel sides times the height?

• Finding the Area of a Regular Pentagon [Gilman, 04/15/1998]
  How can you find the area of a regular pentagon given only the length of one side?

• Constructible Angles and Regular Polygons [Dawson, 04/17/1998]
  What angles and regular polygons are constructible?

• Counting Regions Formed by Straight Lines [Shah, 04/18/1998]
  How many regions are formed by n straight lines if no three meet in a single point and no two are parallel?

• Volume of a Sphere [Fishman, 04/21/1998]
  Can you help me derive and prove the formula for the volume of a sphere?

• Connected Sets in Topology [Flowers, 04/22/1998]
  Exploring connected sets with examples in Euclidean space.

• Intersecting Vectors and the Dot Product [Lu, 04/24/1998]
  Each of the following geometrical theorems can be proved with vectors, using the dot product...

• Deriving the Hyperbola Formula [Gauteaux, 04/27/1998]
  When speaking of hyperbolas, why does C^2 = A^2 + B^2?

• Trigonometry in the Third Dimension [Witty, 04/30/1998]
  How does trigonometry change when we move into the third dimension?

• Finding the Height of a Tetrahedron [Jones, 05/03/1998]
  Using properties of medians, altitudes, and angle bisectors to find the height of a tetrahedron of equilateral triangles.

• Linear and Circular Parametric Equations [Preston, 05/05/1998]
  Using parametric equations to plot a line segment connecting any two points on the plane.

• Deriving the Volume of a Frustum [Taylor, 05/06/1998]
  Can you derive the formula for the volume of a frustum of a cone?

• Differentiating and Integrating the Formula for Area of Circle [Bohanon, 05/11/1998]
  The formula for a circle's circumference is the derivative of the formula for its area. What is the significance of this?

• Diameter of a Circle Circumscribed Around a Triangle [Hicks, 05/13/1998]
  Applying the Pythagorean Theorem to find the diameter of the circle circumscribed around a triangle with side lengths 25, 39, and 40.

• Constructing a Line to Divide Area of a Triangle in Half [Rabiroff, 05/13/1998]
  Cutting a triangle into two pieces of equal area by drawing a a line parallel to one of the sides.

• Congruent and Similar Triangle Theorems [Crane, 05/14/1998]
  Why isn't there an Angle-Angle-Angle (AAA) triangle congruencey theorem?

• The Angle Bisector and Equal Side Ratios [Yerep, 05/17/1998]
  Given a triangle ABC and angle bisector BD, how do you show that AB/AD = BC/CD ?

• Parallel Lines in Projective Space [Hernandez, 05/18/1998]
  Do parallel lines intersect at infinity? Is this in projective space?

• Counting Regions Formed by Chords of a Circle [Shah, 05/19/1998]
  Determining the number of regions formed by connecting n points on the circumference of a circle.

• Great Circle Parametric Equation [Lotter, 05/25/1998]
  How can you calculate specific points of a great circle on a sphere? Can you help me find the parametric equation?

• Understanding Non-Euclidean Geometry [Nestorowicz, 05/26/1998]
  Can you explain about geometries that are not on the plane? For example, what is a straight line on any surface?

• Surface Area and Volume: Cubes and Prisms [Brittani, 05/27/1998]
  What is the definition of surface area and volume? What are the differences and similarities between surface area and volume?

• Lateral Area of Oblique Cones [Elbert, 05/27/1998]
  Can you find a formula for the lateral/surface areas of oblique cones?

• What is an N-gon? [Missy, 06/01/1998]
  Can you explain the statement: "In an N-gon, n-3 diagonals can be drawn from one vertex"?

• The Figure of Maximum Area and Given Perimeter [Morris, 06/02/1998]
  Can you help me show, with and without calculus, that the geometric figure of a maximum area and given perimeter is a circle?

• Constructing a 45-degree Angle [Lily, 06/02/1998]
  How do you construct a 45-degree angle with only a compass and a straightedge?

• Euler Line [Christen, 06/08/1998]
  What is the Euler line?

• Surface Area of a Cone [Schultz, 06/18/1998]
  What is the formula for the surface area of a cone?

• Is Pi a Constant in Non-Euclidean Geometry? [Harper, 06/26/1998]
  What if the circle is stretched across a curved surface?

• Equilateral Triangle: Area Formula and Proof [Andy, 06/16/1998]
  Is there a formula to find the area of an equilateral triangle given a point on its interior and the lengths of the segments from the point to the three vertices?

• Understanding Fourth Dimension Figures [Heidi, 07/05/1998]
  Can you help me figure out the equations for fourth dimension figures such as the tesseract and the hypertetrahedron?

• One More Point Than a Line [Pascual, 07/05/1998]
  In terms of 1-1 correspondence, why does a circle have one more point than a line?

• The Angles of a Tetrahedron [Bryan, 07/08/1998]
  Why is the angle from one vertex to the exact center of the tetrahedron around 109.5 degrees?

• The Height of a Distant Tree [Kostia, 07/08/1998]
  If a tree is 1 mile away, and I see it as 5 cm tall, how can I find its real height?

• Two Problems on Tangents [Wah, 07/09/1998]
  How can you show that the arc and the angle formed by two tangents are supplementary? Find the radius of circle O, given the following...

• Using Vectors in Geometry and Physics [Jenna, 07/10/1998]
  How do you use vectors in problems about medians, areas, and acceleration and velocity?

• Angles of a Cyclic Quadrilateral [Yan, 07/14/1998]
  ABCD is a cyclic quadrilateral with AB parallel to DC. Angle DAC = 40 degrees...

• Spaces Formed by Intersecting Planes [Brooks, 07/19/1998]
  Do you know of a proof that would be used to show how many spaces can be formed by the intersecting of five planes in space? n spaces?

• Angles of an Octahedron [Phani, 07/20/1998]
  What is the angle between two adjacent faces of an octahedron?

• Euler Line and Nagel Point [Wanwipa, 07/20/1998]
  Can you provide more information on the Euler line and the Nagel point, including proofs?

• Properties of Equilateral Triangles [Khaliah, 07/20/1998]
  If ABC is equilateral and AD is one of its heights, what are the measures of the angles? Is ADB equal to ADC? If AB = 2 find BD and AD.

• Vectors of Parallelograms and Octagons [Li, 07/28/1998]
  ABCDEFGH is a regular octagon and AB = p and BC = q. Express AH in terms of p and q...

• Drawing Diagrams [Emma, 08/02/1998]
  I'm having trouble drawing a good geometry diagram.

• Truncating Platonic Solids [Nomura, 08/04/1998]
  What effect does truncation have on Platonic solids? What are some historical and current applications?

• Snub Cube [Vaughan, 08/08/1998]
  What is a snub cube?

• Diameter of the Base of a Cone [Brown, 08/12/1998]
  How do you find the formula to calculate the diameter of the base of a cone of nine degrees at various lengths?

• Approximating Pi using Geometry [Ghosh, 08/12/1998]
  I need to know a simple method to find the approximate value of pi using elementary geometry.

• Two Column Proof of a Theorem [Pendrys, 08/12/1998]
  Write a two-column proof and give numbered statements with reasons....

• SSA and Non-congruent Triangles [White, 08/13/1998]
  Why can't you conclude that two triangles are congruent when side- side-angle are congruent?

• Calculating the Radius from a Chord [Auer, 08/18/1998]
  If I know the chord length and chord height, is there a formula for determining the radius of the circle?

• Coordinate Geometry [Yi, 08/21/1998]
  Given two coordinate points in the cartesian plane, locate a third point perpendicular to the line joining points 1 and 2 and a certain from either point.

• Intersecting Angles [Todd, 08/26/1998]
  Draw a diagram in which the intersection of angle AEF and angle DPC is ray ED.

• Pick's Theorem, Lattice Points, and Area [Sen, 08/27/1998]
  What is a lattice point, and how does it relate to the area of a triangle, rectangle, and a circle?

• Equations in Intercept Form [Cole, 08/27/1998]
  Show that an equation for a line with nonzero x- and y-intercepts can be written as x/a + y/b = 1...

• Flattened Cone [Baker, 08/30/1998]
  Drawing a shape you could cut out and roll up to form a cone whose cross-section you are given.

• Lattice Points and Boundary Lattice Points [Doria, 08/30/1998]
  What is an interior lattice point and a boundary lattice point of a given shape (triangle, circle, rectangle, etc.)?

• Area of a Regular Octagon [Park, 08/31/1998]
  A proof of the formula.

• Volume of a Pyramid [Terence, 09/01/1998]
  How can you prove algebraically and geometrically that the volume of a pyramid is (1/3)b*h?

• The Napoleon Point and More [Schultess, 09/04/1998]
  How do you prove that the Napoleon point will always exist, given the proper conditions? Is there a stronger theorem?

• Distance From a Point to a Line [Keehn, 09/16/1998]
  Derive an equation to give the distance from any point on a 2D plane to a line.

• Naming the Isosceles Triangle [Harris, 09/23/1998]
  How did the isosceles triangle receive its name?

• Rhumb Lines and Great Circle Routes [Leeds, 09/24/1998]
  Can you explain great circles and rhumb lines and how they relate to shortest distances in geometry?

• Parallel Lines and Transversals Proof [Chan, 09/28/1998]
  Prove: If two angles are cut by a transversal and the same-side angles are supplementary, then the lines are parallel.

• Complementary and Supplementary Angles [Saunders, 09/30/1998]
  Why are angles called complementary and supplementary?

• The Origin of Conic Sections [Gray, 10/02/1998]
  What are the origins of conic sections?

• Cutting a Triangle into Two Congruent Triangles [Auerbach, 10/06/1998]
  How do you cut a triangle into two congruent equilateral triangles with the minimum number of cuts?

• Intercept Equation [Sara, 10/07/1998]
  I found a plane using the intercepts (4,0,0), (0,-5,0), and (0,0,3). Now I want an equation for those points using Ax + By + Cz = D.

• Maximum Number of Intersections of n Distinct Lines [Sally, 10/07/1998]
  Find a pattern for the maximum number of intersections of n lines, where n is greater than or equal to 2.

• Pascal's Theorem [Saleh, 10/07/1998]
  Can you explain Pascal's Theorem? How does it relate to conic sections?

• Volume of an Elliptical Cone [Francesca, 10/15/1998]
  Can you help me on find the volume for an elliptical cone by using a triple integration?

• Non-parallel Glide Reflections [Shubert, 10/21/1998]
  A glide reflection consists of a line reflection and a translation parallel to the reflection. What if the translation is not parallel to the reflection?

• CADAEIBFEC and Other NCTM Questions [Moreno, 10/27/1998]
  CADAEIBFEC is a mnemonic for an important piece of mathematical information. What is it?

• Proofs with Isosceles Triangles [Molly, 10/28/1998]
  What are altitudes, angle bisectors, and medians? How do you prove that in an isoseles triangle, the altitude is a median and an angle bisector?

• Geometry and Soccer balls [Monaghan, 10/29/1998]
  I'm looking for ideas for a geometry and soccer bulletin board.

• Ratios and Geometry [Blackwood, 10/29/1998]
  An airplane flying at 33,000 feet has a visibility of 100 miles. What percent of the total land area to the horizon is visible?

• Largest Triangle in a Square [Lee, 10/31/1998]
  If the area of a square is 1, what is the largest area of a triangle constructed inside the square? How would you prove it?

• Ludolph van Ceulen and Pi [Hammond, 11/02/1998]
  How did Ludolph van Ceulen estimate pi by inscribing and circumscribing a circle with squares?

• Definition For Cylinder Without Big Words [Bowden, 11/03/1998]
  I just need a good definition for cylinder that I can understand.

• Find the Orthocenter [Phil, 11/04/1998]
  Given three points (-2,4) (7,2) (3,8), find the orthocenter.

• Geometry Proofs: Lines and Planes [Jaclyn, 11/08/1998]
  Show that two intersecting lines intersect in exactly one point...

• Definitions of Advanced Concepts [Morrison, 11/13/1998]
  Can you give me definitions for: Pythagorean Triplets, Principle of Duality, Euclid's Elements, Cycloid, Fermat's Last Theorem?

• Length of a Copper Helix [Kim, 11/15/1998]
  Can you help me find a formula to determine the length of straight wire needed to form a helix of a certain length when twisted with another wire?

• Types of Tessellations [Siegel, 11/15/1998]
  I am doing a project on tessellations. Can you explain some of the mathematics behind them?

• Congruent Triangles - SSS Test [Dreusch, 11/16/1998]
  How do you know if two triangles are congruent?

• Similar Triangles and Area [Anna, 11/17/1998]
  P is a point on the segment joining midpoints D, E of the sides AB, AC of a triangle ABC. Prove that BPC has twice the area of ADE.

• Graphing an Ellipse [Phil, 11/20/1998]
  How do you graph an ellipse? What is the equation?

• Derivations of Heron's Formula [Hath, 11/24/1998]
  How is Heron's formula (Hero's formula) derived?

• Angle Measurements of Triangles inside Semicircle [Braha, 11/26/1998]
  If the area of a triangle inside a semicircle is equal to the area outside the triangle within the semicircle, then find the values of the acute angles in the triangle.

• Geometric Proofs [Haggarty, 11/28/1998]
  I am tring to help a friend learn geometric proofs. Do you have any suggestions?

• Reflex Angle [Shariff, 11/30/1998]
  What is a reflex angle?

• Which Quadrant in the Unit Circle? [Rosalynn, 11/30/1998]
  Find the quadrant in which C(s) is located. Example: C(14pi/3)= C(2pi/ 3). Thus, C(14pi/3) is in quadrant II.

• Area of Inscribed Circle [Anna, 12/01/1998]
  Find the area of the circle inscribed in a triangle ABC using Heron's Law.

• Acute Angles in a Triangle [Vanderspank, 12/02/1998]
  What is the greatest number of angles smaller than a right angle that a triangle can have?

• An Ellipse Or A Circle? - Parametric Equations [Sands, 12/05/1998]
  Is this parametric equation elliptical or a circle?... And how do I compute the slopes at points 0, pi/4, pi/2, 3pi/2,and 2pi?

• Perimeter of an Inscribed Regular Polygon [Willems, 12/10/1998]
  What is the formula for the perimeter of a regular polygon inscribed inside a circle?

• Straightedge and Compass Constructions [Ross, 12/14/1998]
  Can you help me with these constructions, using only a straightedge and a compass? A 30, 60, 90 triangle, the three medians of a scalene triangle,...

• Determinants and the Area of a Triangle [Chiaravalli, 12/14/1998]
  Given a triangle with vertices (A,B), (C,D), and (E,F), how do you find the area in determinant form?

• Desargues' Theorem and SSASS [Walsh, 12/15/1998]
  What is the main theory behind Desargues' Theorem? Also, is SSASS a valid method for proving two quadrilaterals are congruent?

• Trisected Hypotenuse of a Triangle [Nuse, 12/20/1998]
  In right triangle ABC, with C as the right angle... what is the length of AB (the hypotenuse)?

• Two Circles, Four Tangents, Collinear Midpoints [Ho, 12/20/1998]
  Given two circles that do not touch there are four distinct tangents common to both circles. Prove that the midpoints of the tangents are collinear.

• Pythagorean Theorem - Euclid's Proof [Gayle, 12/27/1998]
  A detailed explanation of a specific proof.

• The Importance of Geometry Constructions [Kel, 12/29/1998]
  Why are geometry constructions important? What do we learn from them? Where have they appeared in math history?

• Parallel Lines [McHatton, 12/31/1998]
  What are some ways of proving lines parallel - geometrically and algebraically?

• Angles Greater than 360 Degrees [Queenie, 01/01/1999]
  We know the definitions of acute, obtuse, and reflex angles, but we were debating what kind of angle a 425 degree angle is.

• Proofs and Reasons [Maggy, 01/03/1999]
  Write a two-column proof for the following theorem: AC is greater than BC and AP = BQ.

• Barycentric Calculus [Noble, 01/06/1999]
  How does barycentric calculus compare with trilinear or cartesian calculus?

• Hexagon vs. Hexagram [Vasquex, 01/11/1999]
  What is the difference between a hexagon and a hexagram?

• A Right Triangle of Points [Strenz, 01/14/1999]
  Determine the values of x that would make the points (x,0), (-2,1), and (3,4) the vertices of a right triangle.

• A Project on Cycloids [Jenny, 01/16/1999]
  Can you explain cycloids? How do you work with the parametric equations? What are their properties? How are they related to time?

• Vector Proofs [Olivia, 01/17/1999]
  Prove that given P, Q, R, and S (any 4 non-collinear points), with A and B the midpoints of PR and QS respectively, then PQ + RS = 2 AB...

• Types of Cones [Rowan, 01/19/1999]
  Does a cone have an edge? Does it depend on what type of cone you have? What are the different types of cones?

• Hyperbolic Geometry and the Euclidean Parallel Postulate [Nelson, 01/20/1999]
  When is it true that, given a line L and a point P, there is an infinite number of lines passing through P parallel to L?

• Vector Proofs [Kwong, 01/20/1999]
  Use vectors to prove that the diagonals of a parallelogram bisect each other and the line joining the midpoints of two sides of a triangle...

• Inscribed Angle Theorem [Darren, 01/21/1999]
  Can you help me prove that an angle inscribed on the same arc as a central angle is equal to one half that central angle?

• Involute of a Circle [Malone, 01/22/1999]
  What is the formula for the involute of a circle?

• Menelaus's Theorem [Wanwipa, 01/25/1999]
  A straight line intersects sides AB, BC and the extension of side AC of a triangle ABC at points D, E and F respectively. Prove that the midpoints of the line segments DC, AE and BF lies on a straight line.

• Midpoint Formula for any Fraction [T.J., 01/26/1999]
  Is there a formula similar to the midpoint formula to find "any fractional part" of the line from P1 to P2?

• Constructing the Orthocenter [Justin, 01/27/1999]
  How do you construct the orthocenter of a triangle?

• Steiner-Lehmus Theorem [McIntosh, 01/28/1999]
  I have a proof about an isosceles triangle that I just can't figure out...

• The Order of a Proof [Stan, 01/29/1999]
  How can you figure out what order to put your proof in?

• Mid-segment Theorem [Richard, 02/02/1999]
  Can you help me prove the Mid-Segment Theorem?

• Nonconvex Polygon Angle Measure [Hartman, 02/03/1999]
  What is the formula to find the interior angle measurements of a nonconvex polygon?

• Moment of Inertia of a Solid Cone [Anonymous, 02/03/1999]
  Find the Moment of Inertia of a solid cone in terms of its height and base.

• Multidimensional Calculus and Vector Geometry [Thomssen, 02/09/1999]
  The depth of iron ore can be approximated by a plane...

• Pole in a Box [Ravi, 02/09/1999]
  Can a pole 6.5m long fit into a truck with dimensions of 3m, 3.5m, and 4m?

• Lateral Surface of a Cone [Grant, 02/10/1999]
  How do you find the formula for the lateral surface of a right cone?

• Ratio of Sides and Ratio of Areas [Bradley, 02/11/1999]
  If the sides of a triangle are in the ratio of 1:7, what is the ratio of their areas? What about for other shapes?

• A Point in the Triangle [John, 02/12/1999]
  Finding the point P in a plane of triangle ABC, where PA + PB +PC is minimum.

• 30-60-90 and 45-45-90 Triangles [Kristina, 03/15/1999]
  If I have a triangle that is 30-60-90 or 45-45-90, how do I find all the sides when given only one side? Where does trigonometry come in?

• Accurate Drawing of an Ellipse [Patrick, 02/14/1999]
  Draw an ellipse accurately using simple tools.

• A Proof using Analytic Geometry [Ngu, 02/24/1999]
  Prove that, if p is a point inside the ellipse, there is one and only one chord QP bisected at P.

• Volume of a Cone [Jodi, 02/19/1999]
  Prove that the volume of a cone is one-third that of a cylinder with the same height and radius.

• Cutting a Sphere [Nick, 02/18/1999]
  How can I cut a sphere into an odd number of pieces?

• Cutting a Cylinder out of a Sphere [Minesh, 02/25/1999]
  What is the remaining volume after a cylinder of length 6" has been cut through the centre of a sphere?

• Medians of a Triangle [Jin, 02/16/1999]
  Prove that the 3 medians of a triangle divide themselves up into a ratio of 1:2.

• Euler's Nine-point Circle [Asit, 02/21/1999]
  What is the "nine-point circle" problem?

• Liquid in an Elliptical Tank [Tom, 02/28/1999]
  Given any height of liquid, say 3 ft., how can I calculate the volume?

• Sum of Degrees in a Triangle [Dami, 03/03/1999]
  Four proofs that the degrees in a triangle sum to 180.

• 3D Figures and Intersections [Matt, 03/04/1999]
  Determining whether a line and plane intersect, and where, using vectors.

• Ceva's Theorem [Ride , 03/04/1999]
  Prove Ceva's Theorem using vector methods and use it to prove the concurrency of the medians, altitudes, or interior angle bisectors of a triangle.

• Triangle Altitudes [Stephanie, 03/05/1999]
  Prove that the three altitudes of a triangle intersect in a common point.

• Is a Circle a Polygon? [Tyler, 03/07/1999]
  Is a circle a polygon?

• Nets in a Geometrical Sense [Abby, 03/07/1999]
  What is the "net" of a shape?

• Triangle Altitude [Michelle , 03/07/1999]
  Using Heron's formula to find the altitude of a triangle whose dimensions are given.

• Volume of a Dome [Ethan, 03/09/1999]
  Is there a formula for the volume of a dome?

• Polygons and Triangles [Jonathan, 03/09/1999]
  Prove that after splitting a regular n-polygon into n triangles, the isosceles triangles have greater area than the scalene triangles.

• Regular and Non-regular Polygon Areas [Robert, 03/10/1999]
  Given a regular and a non-regular polygon with the same perimeter, prove that the area of the regular polygon will always be greater.

• Ellipse Equation [Patrick, 03/11/1999]
  How do I get the equation of an ellipse, given four points and the inclination of the major axis?

• Intersection Points [Sara, 03/13/1999]
  A line goes through the point A(1, 2) to cut 2y = 3x-5 at P and x+y = 12 at Q. If AQ = 2AP, find the coordinates of P and Q.

• Pi and Polygons [Eric, 03/14/1999]
  Derive a formula to find the angle of an n-sided polygon with x sides.

• Constructing a Tangent to a Circle [Lopez, 03/19/1999]
  Construct a tangent to a circle through a given point not on the circle.

• Triangle and Interior Point [Tang, 03/23/1999]
  Let P be a point inside triangle ABC. AP, BP and CP meet three sides BC, CA and AB at R, S and T, respectively...

• Circle Center's Cartesian Coordinates [Cuartiella, 03/24/1999]
  How do you find the Cartesian coordinates of a circle's centers if you know two points on its perimeter?

• Surface Area of a Sphere [Bravo, 03/25/1999]
  How do I calculate the surface area of a sphere?

• An Euler Circle Proof [Gural, 03/26/1999]
  I'm having trouble with the incenter and the inradius.

• Where Will the Runners Meet? [Mize, 03/29/1999]
  Two runners, A and B, start 90 degrees away from each other on a circular track and run at the same speed. If Runner B decides to cut across the track, where will they meet?

• Catenary Curve [Stephen, 03/30/1999]
  Find the vertex of a catenary curve.

• Tangent Line and Circles [Hammond, 04/05/1999]
  Two circles of different radius are tangent to each other. A line is drawn tangent to both circles. How long is the segment between the two points of tangency of the line and the circles?

• Orthic Triangle [Alazah, 04/09/1999]
  How do you find the angles of the triangle ABC, similar to triangle A1B1C1, where AA1, BB1, and CC1 are the altitudes of triangle ABC?

• Point Equidistant from 3 Other Points [Highum, 04/11/1999]
  How do you find a point that is equidistant from three other points?

• Circumscribing Tangent Circles [day, 04/13/1999]
  Given three circles of various sizes in a plane, circumscribe a circle about them.

• Stars in a Flag [Hanlon, 04/15/1999]
  Find the area of the stars in the American Flag.

• Triangle's Medians Make Smaller Triangles with Equal Area [Peurasaari, 04/15/1999]
  Proving that the six triangles constructed from the three medians of any triangle have the same area.

• Inscribing a Regular Pentagon within a Circle [Huang, 04/15/1999]
  What are the reasons for the steps in inscribing a regular pentagon within a circle with only the help of a compass and a straightedge?

• Area of a Segment [Blair, 04/18/1999]
  What are the steps for figuring out the area of a segment of a circle?

• Simson Line [Furman, 04/19/1999]
  What is the Simson line?

• Cone Volume [Shamsi, 04/19/1999]
  A right circular cone is circumscribed about a sphere of radius R cm. Find the ratio of the altitude to the base radius of the cone of largest possible volume.

• Collinearity [Hirsch, 04/20/1999]
  What points in a triangle are known to be collinear with the incenter?

• Map Projections [Sarkissian, 04/26/1999]
  Demonstrate the mathematics of creating a flat map of a curved object.

• A Fibonacci Jigsaw Puzzle [Laik, 04/29/1999]
  Why is the area of our rectangle, formed from a square, 65 when the square's area was 64?

• Height of Parallelogram or Trapezoid [Underwood, 04/30/1999]
  Could you explain the concept of height with regard to a parallelogram or a trapezoid?

• Given a Triangle with Angles a,b,c [kellogg, 05/03/1999]
  Show that cos(a)+cos(b)+cos(c) is less than or equal to 3/2.

• Locus [Jo, 05/03/1999]
  What is a locus?

• Quadrilaterals and Inscribed Circle [Jayant, 05/06/1999]
  From ten sticks of lengths 1,2,3,....,10 four are selected to form the sides of a quadrilateral...

• Pick's and Euler's Theorems [charlie, 05/06/1999]
  What is Pick's theorem and how can it be linked with Euler's theorem?

• Uses of Conics [Martin, 05/09/1999]
  What are some real life examples of conics?

• Vertices in a Prism [Bergner, 05/12/1999]
  What is the formula for finding the number of vertices in a prism?

• Intersecting Circles [Ooi, 05/13/1999]
  A common tangent touches two intersecting circles at S and T. Show that the line AB bisects the common tangent ST.

• 2D and 3D Coordinate Systems [Burda, 05/13/1999]
  I have two 2D coordinate systems S1 and S2 arbitrarily positioned on a plane... determine the relative positions of S2 and S1.

• Rhombicuboctahedron [Jenna, 05/14/1999]
  How can you make a soccer ball out of a particular shape - for example the rhombicuboctahedron?

• Deriving Trilinear Coordinates [Smith, 05/18/1999]
  How do you derive the trilinear coordinates of the orthocenter of a triangle?

• Will the Tree Hit the House? [Madison, 05/18/1999]
  A tree is leaning at 70 degrees, our house is 66 1/2 feet away, and the angle from our house to the top of the tree is 40 degrees...

• Circle Inscribed in Sector [Wipke, 05/20/1999]
  Given a 60-degree arc of a sector of a circle with a radius of 12 inches, find the area of the circle that can be inscribed in the sector.

• Math in soccer [Ricard, 05/21/1999]
  How is math involved in soccer?

• Surface Area of Pyramids [Copley, 05/21/1999]
  We understand how to find the surface area, but we cannot figure out how to determine the slant.

• Distance to the Horizon [Robert, 05/23/1999]
  How far is the horizon?

• Altitudes and Bisectors of a Triangle [Hanna, 05/25/1999]
  Prove that the altitudes of a triangle are bisectors in the triangle formed by connecting the meeting points of the altitudes with the sides of the original triangle.

• Intercept of a Line with a Circle [Doyle, 05/28/1999]
  What is the general equation for the intercept between a circle x^2 + y^2 - 2fx - 2gy + d = 0 and a line ax + by + c = 0?

• Volume of a Sphere [Banijamali, 05/28/1999]
  Why is the volume of the sphere V = (4 Pi/3)r^3?

• Constructing a Pyramid [Daniel, 05/28/1999]
  How can I calculate the sides and angles needed to construct a pyramid with an 8-foot-square base and a height of 6 feet?

• Finding the Center of a Circle [John, 06/01/1999]
  How do you find the centre of a circle if you are given 2 points on the circle and the radius?

• Pi and the Bible [Gibson, 06/01/1999]
  Can you prove that the value of Pi cannot be rounded down to 3.0?

• A Pyramid of Layered Marbles [Chris, 06/02/1999]
  How can I find the number of layers, the number of marbles, and the size of a container containing a pyramid of layered marbles?

• Radius of a Circle Inscribed in a Triangle [Michael, 06/02/1999]
  What is the radius of an inscribed circle of a triangle with sides 3, 4, and 5?

• A 3-D Object that Fits 3 Holes [gretchen, 06/03/1999]
  How can I make an object that can fit in 3 holes of different shapes, blocking all light, and sliding all the way through without forcing it?

• Enlarging the Penguin Pond [Crystal, 06/03/1999]
  By how much should its length and width be increased to double the area of the 12 meter x 8 meter penguin pond at the zoo?

• Lattice Points in a Rectangle [John, 06/04/1999]
  How can I prove that in any rectangle centered at (0,0) with an area greater than 4, you can find lattice points other than (0,0)?

• Surveyor's Formula [Pagani, 06/05/1999]
  Can you give me a method to calculate the area of an irregular polygon given all the coordinates of the points?

• Finding the Center of a Circle [Eddie, 06/06/1999]
  How can I find the center and radius of a circle that is in the form: Ax^2 + Cy^2 + Dx + Ey + F = 0?

• Radius from an Arc and a Chord [Castellano, 06/08/1999]
  If I know the height of an arc from the midpoint on a chord, and the length of the chord, can I find the radius of the circle of which the arc is a part?

• Ratios, Geometry, Trigonometry [Cathy, 06/10/1999]
  A homeschool teacher asks for help with triangles, flagpoles, and circles.

• Maximum Angle between Perpendicular Bisectors [Hommez, 06/11/1999]
  Which four points on the circumferences of two non-intersecting circles will yield the maximum angle between the two perpendicular bisectors produced by their joins?

• Determining Equable Shapes [Jonathan, 06/15/1999]
  Could you please list some equable shapes and show me how you determined them?

• Trisecting an Angle [Kovach, 06/15/1999]
  I've come up with a method of approximately trisecting any angle. Can you tell me how accurate it is?

• How Many Edges in a Circle? [Mayhew, 06/15/1999]
  Are there one, none, or an infinite number of edges in a circle?

• Circle Radius from Chord Length and Depth [Duranleau, 06/16/1999]
  How do you find the radius or diameter of a circle when you only know a chord length and the depth?

• Linear Systems of Equations in Two Variables [Jen, 06/18/1999]
  How can I find the length of AE, EB and DC, given that parallelogram ABCD has a perimeter of 50, trapezoid AECD has a perimeter of 39, and AE = EC?

• Rectangles Inscribed in a Dodecahedron [Condren, 06/19/1999]
  What is the equation for determining the size of the rectangles inscribed within a regular dodecahedron?

• Derivation of the Equation of an Ellipse [Walsman, 06/23/1999]
  How can I derive the equation of an ellipse from its definition?

• Area and Perimeter in Polygons [Hansen, 06/24/1999]
  How can I prove the formula A = (a^2n)/(4tan(180/n)) for computing the area of a regular n-gon with sidelength a? How does this compare to the area of a circle?

• Center of a Circle from Circumference Points [Koch, 06/25/1999]
  How do I figure the center point (Xc,Yc,Zc) of a circle given 2 or more points on its circumference and its radius?

• Tangents to Circles [Thaddeus, 06/25/1999]
  How can I prove that a line L is tangent to Circle C if and only if L is perpendicular to ZA, where Z is the center C and A is a point on C?

• Maximizing the Volume of a Box [Sherrillo, 06/27/1999]
  I have a piece of glass that is 14" by 72". What dimensions would I need to make a glass cage with maximum volume?

• Perimeter of an Ellipse [Lawn, 06/29/1999]
  Is there a formula that gives the exact perimeter of an ellipse?

• Line Tangent to Two Circles [Cruz, 07/01/1999]
  How do you construct a line tangent to two different-sized circles?

• Cutting a Cube [Borris, 07/05/1999]
  How many pieces will there be if you make every (flat) slice through a cube that goes through exactly three of the cube's corners - no more and no less?

• Finding the Length of a Coil [Johnson, 07/07/1999]
  How can I find the length of a coil or spring given the diameter and pitch and number of turns?

• Locating a Ship Using Three Angles [Thaddeus, 07/07/1999]
  A ship's navigator saw landmarks in the distance at points A, B, and C, found angles ASB, BSC and CSA, then located the three points on a map to find the exact position of her ship. How did she do it?

• Hose Length [Terry, 07/11/1999]
  Find the length of a 1" OD hose that is wrapped around a 10-inch cylinder 50 times.

• How Long is the Hypotenuse? [Mann, 07/12/1999]
  In a right triangle, the lengths of the segments connecting the points of trisection of the hypotenuse to the vertex of the right angle are 7 and 9...

• A 'Pyramiddle' Tent Problem [Hufnagel, 07/12/1999]
  Figure out an equation that yields d when values for h and r are inserted.

• Cutting a Square into Five Equal Pieces [Shinichi, 07/12/1999]
  How can you divide a square cake into five equal parts, cutting through the center point?

• Calculus Cylinder-Cone Problem [Drew, 07/13/1999]
  I have to find the altitude of a triangle...

• Perimeter of 1000m [Macdonald, 07/13/1999]
  Find the shape with perimeter 1000m and the largest possible area.

• Three Intersecting Circles [Tom, 07/14/1999]
  Two circles (X^2+Y^2+4X-4Y-8 = 0 and X^2+Y^2-X-Y-2 = 0) intersect at points P and Q. Another circle (3X^2+3Y^2-13X+KY+L = 0) passes through P, Q, and A (3,1). What is L?

• Overlapping Circles [Hastings, 07/14/1999]
  Each of two overlapping circles has a radius of 6 inches. How long is the darkened portion, in inches?

• Three Houses, Three Utilities [Chris, 07/15/1999]
  Can you solve it using 2 dimensions? How?

• Radius and Center of a Circle from 3 Points [Sokalski, 07/23/1999]
  Given the coordinates of three points on a circle, how can you find the center and radius?

• Arcs Inside a Square [Susan, 07/25/1999]
  What is the area of the figure created by the intersection of two arcs drawn in a square of sidelength 5 units?

• Applying Euler's Methods [Cunningham, 07/27/1999]
  Questions about prime divisors, triangle constructions, decomposing quartic polynomials, and rational roots.

• Making Hemispheres out of Paper [Osborn, 07/28/1999]
  How would you make a hemisphere from a piece of paper? Using triangular wedges of 30 degrees?

• Formula for the Trapezoid Rule [Lester, 07/31/1999]
  I am writing a program to find the moment area of any shape...

• Pixels in a Triangle [Cambazoglu, 08/02/1999]
  How can I find the number of pixels inside a triangle?

• Conical Sections [Cope, 08/02/1999]
  If I know the angle and the diameter of one end of a frustum of a cone and the length of the frustum, What is the diameter of the other end of the frustrum?

• Three Spheres in a Dish [Guy, 08/04/1999]
  What is the radius of a hemispherical dish if 3 spheres with radii of 10 cm are inside the dish and the tops of all 3 spheres are exactly even with the top of the dish?

• Do Circles Have Corners? [Tanaka, 08/06/1999]
  Can you have angles or corners without edges?

• Proof of the Parallelogram Law [Kenneth, 08/07/1999]
  How do you prove the parallelogram law geometrically, without using vectors?

• Importance of Reasonable Approximation [Ross, 08/07/1999]
  A stairway profile, and the calculation of arc length and curved surface area.

• Deriving the Midpoint Formula [Kilburg, 08/08/1999]
  How is the midpoint formula is derived from the distance formula?

• Calculating a Mirror's Reflection [Brandon, 08/08/1999]
  How can I find the angle and the point on a mirror to shine a light at in order to illuminate an object?

• Klein Bottles and Mobius Strips [Evans, 08/09/1999]
  How is the Klein bottle related to the Mobius Strip? Why can't I construct a Klein bottle in 3-dimensional space without intersection?

• Derivation of the Formula for the Frustum [Rizza, 08/09/1999]
  Using similar triangles to derive the formula of a frustum of a right circular cone, given the volume of a right circular cone.

• Napoleon's Triangle [Evenson, 08/10/1999]
  What is Napoleon's triangle?

• Converting QBasic Angles to Mathematical Angles [Wigton, 08/11/1999]
  QBasic measures angles clockwise from north, while mathematicians measure them counterclockwise from east. How can I convert QBasic's angle measures to mathematical ones? Also, do negative angles exist?

• Trisecting a Line Segment [Cbr, 08/13/1999]
  How can I measure one-third of a line of an unknown length using a compass and a straightedge?

• Packing Spheres [McLane, 08/16/1999]
  How many 1.68-inch-diameter spheres fit into a 96.3-cubic-foot space? How many 1.68-inch-diameter spheres would fit into a 96.3-foot- diameter sphere?

• Circle Enclosed by Three Circles [Sokalski, 08/18/1999]
  How can I find the center and radius of a circle that is enclosed by three other circles that all touch each other at one point?

• Area of an Ellipse [Turlais, 08/18/1999]
  How do you calculate the area of an ellipse?

• Finding the Intersection of Two Circles [Groff, 08/19/1999]
  How can I find the intersection points of two circles?

• Visualizing a Klein Bottle [Sean, 08/19/1999]
  What part of a Klein bottle can't be seen or represented in 3D? Is there a technique that can help me visualize higher dimensions?

• Area of Polygon [Bachmann, 08/20/1999]
  Using coordinate system to find the areas of polygons.

• Constructing a Triangle [Angel, 08/20/1999]
  How can you construct a triangle with 3 different-size segments?

• Distance from a Point to a Line [Gallagher, 08/20/1999]
  Can you show me a straightforward way to derive the formula for the distance from a point to a line: abs(Ax+By+C)/sqrt(A^2+B^2)=D?

• Surface Area and Volume of a Sphere [Vu, 08/30/1999]
  Besides using integration, is there an intuitive way of seeing why the surface area of a sphere = 4(pi)r^2 and the volume = (4/3)(pi)r^3?

• Volume and Surface Area of a Cone Frustum [Reddy, 08/30/1999]
  Can you show me how the formula for the volume and total surface area of the frustum of a right circular cone is derived?

• Packing 4 Spheres Into a Tetrahedron [Lam, 09/03/99]
  How can I find the dimensions of the smallest tetrahedron that can serve as a container for 4 spheres packed as snugly as possible?

• Volume of a Hemisphere Using Cavalieri's Theorem [Pappas, 09/09/99]
  How can I derive the formula v = (2/3)pi R^3 for the volume of a hemisphere of radius R using Cavalieri's theorem?

• Are All Triangles Isosceles? [Klotz, 09/15/1999]
  Can you help me find the flaw in this 'proof' claiming that all triangles are isosceles?

• Finding Triangle Vertices from Midpoints [Shan, 09/18/1999]
  If you know the coordinates of the midpoints of the sides of a triangle, how can you find the coordinates of its vertices?

• Golden Triangle [Byerly, 09/19/1999]
  What is a Golden Triangle?

• Radius of a Racing Circle [Hocking, 09/20/1999]
  How can I find the equation for the radius of a 'racing circle' (the fastest path a racecar can take through the corner defined by the quadrants of two circles), an arc sandwiched between identical quadrants of two concentric circles?

• Right Triangle Inscribed in a Parabola [Mohs, 09/20/1999]
  Show that the point of intersection Q of the axis of the parabola y=x^ 2 and the hypotenuse of right triangle RST (inscribed in the parabola so that R coincides with the vertex of the parabola) is independent of the choice of right triangle.

• Desargues' Theorem [Rezvan, 09/22/1999]
  What is Desargues' theorem and how can it be proven?

• Constructing a Segment [Medeiros, 09/26/1999]
  Given a 1" segment and a 2.5" segment, how can you find a segment of length sqrt(2.5)" using only a compass and a straightedge?

• Einstein, Curved Space, and Pi [Steve, 10/09/1999]
  If space is curved and Euclidean geometry doesn't apply, doesn't that mean that the value of pi changes and can sometimes be rational?

• Square with Area Equal to a Triangle [Christina, 10/23/1999]
  Given an arbitrary triangle, how can you construct a square with the same area as the triangle?

• Proof of Perpendicularity [Michael, 10/23/1999]
  How can you prove that two lines (neither vertical) are perpendicular if and only if the product of the gradients is equal to -1?

• Triangle: Longest Side Opposite Greatest Angle [Michael, 10/23/1999]
  Prove that in any triangle, the greatest side is opposite the greatest angle.

• Finding the Coordinates of a Triangle Vertex [Madhusudhan, 10/26/1999]
  How can I find the coordinates of the point A of triangle ABC if B lies on the line 3y = 4x, C lies on the line y = 0, the line BC passes through (2/3,2/3) and AOBC forms a rhombus (where O is the origin)?

• Another Isosceles Triangle [Dalal, 10/27/1999]
  A triangle has sides of length 29, 29, and 40 cm. How can I find another isosceles triangle with the same perimeter and area that also has sides of integral length?

• Area of a Regular Octagon [Tahiliani, 10/27/1999]
  How do you find the area of a regular octagon?

• Angle Between Two Sides of a Pyramid [Lukens, 10/29/1999]
  How can I compute the angle formed by two sides of a frustrum of a pyramid?

• Dividing Land by Area vs. Perimeter [Werner, 11/05/1999]
  What are the advantages of dividing land by area versus perimeter?

• Attempt at Trisecting an Angle [Mellon, 11/08/1999]
  Can the arcs of the two circles formed by the construction described be the same length? Would this construction trisect the angle?

• Two-Column Proof About Kites [DeMent, 11/09/1999]
  Can you help me understand a proof about perpendicular lines and congruent triangles in a kite?

• Dissecting a Square into Acute Triangles [Sheraden, 11/09/1999]
  Can you dissect a square into a finite number (fewer than 14) of acute triangles?

• Theorems for Quadrilaterals [Bethmarie, 11/12/1999]
  Methods of proving congruence of quadrilaterals similar to the ASA, SAS, SSS congruence postulates for triangles.

• Characteristics of an Orthocenter [Carbonetti, 11/12/1999]
  What are some characteristics of the orthocenter of a triangle?

• Proving the Existence of the Centroid [Orlando, 11/16/1999]
  How can I prove that the centroid of any arbitrary triangle exists?

• Sum of the Angles in an N-Pointed Star [Ashley, 11/29/1999]
  Can you tell me how to find an equation for the sum of the angles in the tips of an n-pointed star?

• Surface Areas of Soap Bubbles [Alex, 11/30/1999]
  If you build a frame shaped like a tetrahedron and dip it in bubble solution, why do all of the faces of the bubble collapse to a point in the middle of the tetrahedron?

• Volume of an Elliptical Frustum [Macleod, 12/01/1999]
  What is the volume of an elliptical frustum?

• A Triangle with Three Right Angles [Stine, 12/01/1999]
  How can you make a triangle with three right angles?

• One- and Two-sided Polygons [Sue, 12/07/1999]
  Can you explain what a monogon and a digon are?

• Ratio of Volume to Surface Area in Humans [Hall, 12/09/1999]
  What is the healthy ratio of volume to surface area for humans?

• The Spider and the Fly [Keith, 12/23/1999]
  A spider and a fly are on opposite walls of a rectangular room... Does the spider get the fly?

• Classifying Shape Based on Coordinate Points [Freyer, 01/03/2000]
  How can I design an algorithm to classify shapes based on a relatively small set of (x,y) coordinates that describe the boundary of a closed object?

• Incenters, Orthocenters, and the Spieker Point [Wilson, 02/13/2000]
  Prove that the circumcenter of a triangle is the orthocenter of its medial triangle, and that the incenter of the triangle is the orthocenter of the triangle formed by the 3 excenters.

• Counting Intersections of Diagonals in Polygons [Dingena, 03/08/2000]
  Can you help me find an equation for the maximum number of intersections of the diagonals in a polygon?

• Proof of the Feuerbach Theorem [BenAri, 03/14/2000]
  Please submit the proof of the Feuerbach theorem (the nine-point circle is tangent to the incircle and the circumcircle of a triangle.)

• Pythagorean Theorem Proof Explained [Anne, 03/15/2000]
  Could you give me a step-by-step explanation of Dr. Scott Brodie's proof of the Pythagorean theorem given at the cut-the-knot website?

• Steiner-Lehmus Theorem [Karri, 03/24/2000]
  If the lengths of two angle bisectors of a triangle are equal, prove that it is an isosceles triangle; if the opposite angles of a quadrilateral add up to 180 degrees, prove that it is a cyclic quadrilateral.

• Distance to an Object [Pattison, 04/07/2000]
  Is there an easy way to measure the distance from a baseline to an object if one knows the measurement of the baseline and both angles leading toward the object?

• Volume of a Truncated Cylinder [Evans, 05/07/2000]
  How can I find the volume of a cylinder that has had part of its top and bottom removed?

• Volume of Liquid in a Cylindrical Tank [Mustapha, 05/08/2000]
  How can I calculate volume of liquid in a cylinder that's not full and lying horizontally?

• Finding a Plane Shape for a Truncated Cone [Hartman, 05/10/2000]
  What is the best way to cut a flat two-dimensional piece of sheet metal into a three-dimensional truncated cone?

• Area of an Inscribed Quadrilateral [Wallenberg, 05/11/2000]
  Given a quadrilateral where the midpoints of each side are connected to form a new quadrilaterals inside the first, what is the ratio of the area of the larger quadrilateral to the smaller one?

• Volume of a Frustum-Like Structure [Cunningham, 05/12/2000]
  How can I calculate the volume of a frustum-like structure with a rectangular base and rectangular top whose dimensions are: top: 73x37, bottom: 46x10.5, angle: 18 degrees, and height: 4.6?

• Drawing a Circle Tangent to an Angle [Klee, 05/13/2000]
  Given an angle and any point inside it not on its bisector, how can you draw a circle that goes through the point and is tangent to both sides of the angle with just a compass and protractor?

• Reflective Properties of a Semicircular Mirror [Hunter, 05/16/2000]
  What are the reflective properties of a semicircular mirror? Will a ray exit a semicircular mirror parallel to its entry line?

• Two-Column Proof of Congruence [Claire, 05/16/2000]
  How can I complete this two-column geometry proof?

• Surface Area and Volume of a Sphere [Randy, 05/16/2000]
  Without using calculus, how can I show why the coefficient in the formula for the surface area of a sphere is 4, and why 4/3 is the coefficient in the formula for the volume of a sphere?

• Finding Captain Kidd's Treasure [Nilsson, 05/17/2000]
  How can you find Captain Kidd's treasure if you can't find the tree referenced in the instructions?

• Equation of a Line in Three or More Dimensions [Jarosch, 05/18/2000]
  Can the equation y = mx + b be used to define a line in three dimensions? What about four or more dimensions?

• Cyclic Quadrilateral [Cherriblossom, 05/22/2000]
  For an isoscles trapezium ABCD with AB paralled to DC and AB less than CD, how can we prove that ABCD is a cyclic quadrilateral?

• Minimizing the Surface Area of a Can [Donges, 05/22/2000]
  What coke can dimensions would use the least amount of aluminum while still holding 375 ml?

• Finding the Center of a Circle From Three Points [Furst, 05/22/2000]
  How can I find the coordinates of the center of a circle, given the coordinates of three points on its circumference?

• Curvature of Non-Euclidean Space [Rosenof, 05/22/2000]
  What is the difference between positive and negative curvature in non- Euclidean geometry?

• Finding the Base of Parts of a Triangle [Pawlewski, 05/22/2000]
  Can you derive an expression for L1 in terms of L2 and L3 such that the area of a triangle with base A1 and the area of a triangle with base A2 are each 10% of the total area?

• Left-Sided Rhombuses in a Larger Rhombus [Wright, 05/22/2000]
  How many left-sided, right-sided, and vertical rhombuses can be found in a larger NxN rhombus?

• Mutually Tangent Circles [Brian, 05/22/2000]
  Circles A, B and C are mutually tangent and each is tangent to line DFE at points D, F and E respectively. What is the radius of C as a function of the radii of A and B?

• Length of the Diagonals of a Parallelogram [Moose, 05/22/2000]
  A parallelogram has a 70-degree angle and sides 6cm and 10cm long. How long are its diagonals?

• Pedan Trapezium [Cherriblossom, 05/23/2000]
  How can I prove that a isosceles trapezium whose parallel side lengths are 7 and 4 respectively, and whose slant sides have length 6, is a Pedan trapezium?

• Diameter of Cone Frustum [Vin, 05/24/2000]
  Given the inner and outer diameters and the height of a cone frustum, how can I find the diameter when it is opened up flat?

• Measuring the Height of a Building Using Shadows [Rapp, 05/24/2000]
  What time of day is best to use a shadow to measure the height of a building by using triangles?

• Finding the Center of a Circle Given 3 Points [Jaworski, 05/25/2000]
  How can I find the coordinates of the center of a circle given the x and y coordinates of 3 points that lie on its circumference?

• Constructing a One-Degree Angle [Callanta, 05/25/2000]
  Is it possible to contruct a one degree angle using only a straightedge and compass?

• Area of an Ellipse Cut by a Chord [Jordan, 05/26/2000]
  How can you calculate area of the part of an ellipse cut off by a chord, if you know the major and minor axes, and the chord?

• A Triangle in a Circle [Gamache, 05/26/2000]
  Suppose you randomly place 2 points on the circumference of a circle. What is the probability that a 3rd point placed randomly on the circle's circumference will form a triangle that will contain the center of the circle?

• Converse of the Parallel Lines Theorem [Sarah, 05/28/2000]
  How can I prove the converse of the Parallel Lines Theorem: If a transversal intersects two lines so that the alternate angles are equal, then the lines are parallel?

• Medians of Triangles Proof [Jenny, 05/29/2000]
  Prove that in any triangle, the sum of the medians is more than 3/4 of its perimeter, but less than the whole perimeter.

• Teaching about Bearings [Widdicombe, 06/08/2000]
  What are bearings? Do you have any ideas on how I can present bearings to my math class in an interesting fashion?

• Tanker Bearings [Crane, 06/11/2000]
  From ship A, the bearing of an oil tanker is 300 degrees; from ship B, 1000 m due west of A, the bearing of the tanker is 060 degrees. Is the oil tanker the same distance from A as from B?

• Trisecting an Angle [Vatis, 06/17/2000]
  I believe I have a simple straightedge and compass construction that trisects any angle except a right angle, but have not been able to write a proof...

• Radius of the Earth as an Ellipsoid [St. Amand, 06/26/2000]
  I have been given two equations to determine the radius of the earth for a given latitude, based on ellipsoid model WGS84. I get different answers...

• Definition of a Cone [Romanowski, 07/13/2000]
  I don't see how a right circular cone cut parallel to the axis of symmetry reveals a hyperbola. Shouldn't it be a parabola?

• Proof of Morley's Theorem [Karamalizadeh, 08/09/2000]
  How can I prove Morley's theorem (if every angle in a triangle is trisected, each pair of trisectors meets in a point, and all three points form the vertices of an equilateral triangle)?

• Apollonius' Problem [Cottaar, 09/07/2000]
  Given three circles, is it possible to construct a circle tangent to each of them using only a compass and straightedge?

• De Longchamp's Point [Zencka, 09/21/2000]
  What is De Longchamp's point, and how is it used?

• Circles within a Circle [Brian, 10/12/2000]
  Given three circles of diameters 3", 2", and 1", the two smaller inside the largest so that their combined diameters equal the diameter of the largest circle. What is the greatest possible diameter of a fourth circle placed in the remaining area?

• Inscribing a Square in a Triangle [Alexandra, 10/13/2000]
  How do you inscribe a square in a scalene triangle?

• The Erdos-Mordell Theorem [Zacks, 10/13/2000]
  Let P be a point in a triangle, D be the sum of the distances from P to the 3 vertices, and E be the sum of the distances from P to the edges. How can I prove that D is greater than or equal to 2*E?

• Flattening the Frustum of a Cone [Scholl, 10/15/2000]
  We are building a desk the front of which forms a section of a cone. We know the radius and chord length at the top and the floor. How do we generate a flat layout of this section?

• A Ladder Puzzle [Dueck, 10/20/2000]
  A 10-meter ladder is leaning against a wall just touching the corner of a 3-meter cube placed flat against the wall. At what height does the end of the ladder touch the wall?

• Applications of Parabolas [Lau, 10/24/2000]
  How are parabolas used in real life?

• Formulas for N-Dimensional Spheres [Weeks, 10/26/2000]
  What is the next term in the sequence pi*r^2, (4/3)pi*r^3, ...? Would it be the formula for the volume of a 4-dimensional sphere?

• Volume of Intersecting Pipes [Sam, 10/27/2000]
  How can you calculate the volume of the intersection of two perpendicular pipes of the same radius?

• Surface Area and Volume Derivative [Mike, 10/30/2000]
  For what 3D figures is the derivative of the volume formula equal to the formula for surface area? With respect to which variable would you need to differentiate?

• Area of a Crescent [Graham, 11/10/2000]
  What is the formula for the area of a crescent?

• Volume of a Trapezoidal Solid [Greg, 11/15/2000]
  How can I find the volume of a figure formed by two aligned noncongruent rectangles connected by planes?

• Area of a Segment from Arc and Chord Length [Castricone, 11/27/2000]
  How do you find the area of a segment of a circle if you know only the arc length and chord length?

• Bretschneider's Theorem and Cyclic Quadrilaterals [Blumberg, 11/30/2000]
  Can you prove Bretschneider's Theorem for the area of a quadrilateral? Also, can you show that any quadrilateral with supplementary opposing angles can be inscribed in a circle?

• Volume of a Spherical Cap [Reid, 12/06/2000]
  How can you derive the formula for the volume of a spherical cap without using calculus?

• Mixtilinear Incircle Proof [Ailette, 12/11/2000]
  In triangle ABC, AB = AC. A circle is tangent internally to the circumcircle of triangle ABC and also to sides AB and AC at points P and Q, respectively. How can I prove that the midpoint of the segment PQ is the center of the mixtilinear incircle of triangle ABC?

• Voronoi Diagrams [Karl, 12/12/2000]
  On a Voronoi diagram, how do you know which lines and which parts of those lines you need?

• Hinge Theorem [Gina, 12/12/2000]
  How would you write a proof for the Hinge theorem?

• The Value of Two-Column Proofs [Patrick, 12/19/2000]
  What is the point of learning two-column proofs?

• How Many Points Determine a Parabola? [Ramani, 12/20/2000]
  How can we determine whether or not a given plane curve is a parabola? Under what conditions is a parabola uniquely determined?

• Constructing a Triangle Given the Medians [Ali, 01/01/2001]
  How can I construct a triangle ABC given AM, BN, and CP, the respective medians from the vertices A, B, and C?

• Minimal Distances to a Point in a Triangle [Shin, 01/05/2001]
  How can I prove that the smallest value of PA + PB + PC occurs when angle APB = angle BPC = angle CPA = 120 degrees, for a triangle ABC and a point P?

• Folding a Circle to Get an Ellipse [Rosin, 01/08/2001]
  How can I prove that taking a point on a circle, folding it to an interior point, and repeating this process creates an envelope of folds that forms an ellipse?

• Compound Angles [Mangwiro, 01/14/2001]
  A rail does not go into a post horizontally, but has a rise angle of 30 degrees and a side angle of 39 degrees. The hole to be routed needs to be a parallelogram instead of a square...

• Volume of a Rhombicuboctahedron [Nicoal, 01/19/2001]
  What is the formula for finding the volume of a polyhedron called a rhombicuboctahedron?

• Ant and Rectangle [Li, 01/22/2001]
  Does the ant walk along the diagonals of the rectangle?

• Golden Triangle [Connors, 01/23/2001]
  What is the Golden Triangle?

• Circumference at a Given Latitude [Lynn, 01/26/2001]
  How can I calculate the circumference of a line around the earth (a circle) at 40 degrees north latitude?

• Finding the Axes of an Ellipse from a Known Cone [Mion, 01/26/2001]
  I'm trying to solve a specific situation regarding lighting when viewed as an oblique circular cone...

• Building a Wooden Square-Based Pyramid [Hosler, 01/26/2001]
  I want to build a wooden pyramid with a square base 8"by 8".

• Circle Regions [Buerkel, 01/28/2001]
  What is the maximum number of regions you can have with n chords in a circle?

• Volume of a Cone [Cari, 01/29/2001]
  I know HOW to find the volume of a cone (1/3area of base times height divided by three) but my teacher wants to know WHY...

• Lines of Symmetry [Laura, 01/29/2001]
  How do you find the number of lines of symetry there are in a polygon?

• Calculating Circle Radius [Galloway, 01/29/2001]
  I am trying to find a formula that will give me the radius of a circle, given only the length of an arc on that circle and the chord length of that arc.

• Taping a Cylinder [Robinson, 01/29/2001]
  If I want to wrap sticky tape around a cylinder to cover it, what is the relation between the diameter of the cylinder, the thickness of the tape, and the angle between the diameter of the cylinder and the length of the tape?

• Square Inside a Square [Kohn, 01/30/2001]
  Imagine a square with eight compass points marked at each corner and midpoints of the sides. Create a smaller square inside... How do the areas of the two squares compare, and why?

• Is This a Square? [Greg, 01/30/2001]
  Given four points on a graph, what can I do to verify this is a square?

• Uniquely Determining a Polygon [Gaston, 02/05/2001]
  Is it true that if you know the side order, side lengths, and area of a polygon, as well as whether each of its angles is obtuse or acute, you have uniquely determined it?

• Longitude-Latitude Product and Distance [Abdullahi, 02/14/2001]
  Is the difference between the product of the longitude and latitude of one point and that of another point related to the distance between them?

• Pattern for Lampshade [Loraine, 02/17/2001]
  I would like to know the formula for computing the surface area of a lamp shade so that I can make a pattern from it.

• Numbering the Faces of Dice [Cotterill, 02/27/2001]
  How many ways are there to make dice out of the Platonic solids (i.e. 4, 6, 8, 12, and 20 sides)? How many of those ways have opposite face sums equal? What would the opposing face sums be for each type?

• Area under Arc of Circle [Drapeau, 02/27/2001]
  Calculate the area delimited by the arc of a circle and the chord of that arc, given only the length of the chord and the length of a line, perpendicular to the chord, running from the middle of the chord to the edge of the circle.

• Semicircle Proof [Vmadhulika, 02/27/2001]
  M is the midpoint of AB. Three semicircles with diameters AM, MB, and AB are drawn. A circle with centre O and radius r touches all three. Prove that r = 1/6 AB.

• Surface Area of an Egg [Sean, 02/28/2001]
  How do you find the surface area of an egg?

• Apollonian Construction Problem [Knight, 03/06/2001]
  Given a line and two points A and B, construct a circle tangent to the line and containing the two points.

• A Practical Use for the Orthocenter [Hodel, 03/07/2001]
  Does the orthocenter of a triangle have any practical uses?

• Dividing a Line Segment [Lemke, 03/08/2001]
  How do I divide a line segment into a 2:3 ratio using the angle bisector?

• Triangle Inequality Theorem [Cprime, 03/09/2001]
  The lengths of the sides of a non-isosceles triangle, in size order, are 5, x, and 15. What are all possible integral values of x?

• Lines of Symmetry in Regular Polygons [Wendy, 03/13/2001]
  Is there a formula for finding all the lines of reflectional symmetry in regular polygons?

• SSA Proof [Brent, 03/14/2001]
  Proving congruence using the Side-Side-Angle Theorem.

• Fabric Left on a Roll [Rob, 03/15/2001]
  I am going to write a program for my TI-83+ to calculate how many feet of material are left on a roll.

• Ladder Puzzles [Chamberlain, 03/16/2001]
  Two ladders are leaning opposite ways between two buildings... at what height above the ground do they cross? How wide is the alley?

• Topology [Shumi, 03/19/2001]
  What is topology?

• Volume of a Frustum Cone [Randy, 03/20/2001]
  Given a frustum cone with a bottom radius of 4", a top radius of 2", and a vertical height of 12", find the interior heights if the volume is divided into equal thirds.

• Apothem of a Triangle [Anne, 03/21/2001]
  Find the apothem and radius of a triangle with a side of length 12.

• Slicing Up a Circle [Don, 03/22/2001]
  Find a formula that will give the maximum number of pieces with n number of straight slices of the circle.

• Find Angles, Area, Perimeter of a Parallelogram [Jamie, 03/23/2001]
  I can't understand how to find indicated measures when I am given little information to begin with.

• Incircles Tangent to a Common Line [Klein, 03/23/2001]
  In triangle ABC, the incircle touches side AB at M. T is an arbitrary point on BC. How can I show that the incircles of triangles BMT, AMT and ATC are all tangent to a common line?

• Proof: Median of a Trapezoid Theorem [Heather, 03/24/2001]
  Prove that the median of a trapezoid is: 1) parallel to its bases; 2) length = 1/2 the sum of the bases.

• History of Abscissa [Fogelfis, 03/26/2001]
  Where does the word abscissa come from?

• Programming the Distance Formula [Payette, 03/26/2001]
  I want to write a computer program to find the point on a line that's a distance X from a given point not on the line. Can you help?

• Dividing a Square in Thirds [Prager, 03/27/2001]
  How can I divide a square into three equal pieces using three lines radiating from the center of the square?

• Same Surface Area and Volume [Solis, 03/28/2001]
  How can I find two objects of the same type of shape with the same surface area but different volumes? For example, two rectangular prisms or two cylinders?

• How Many Dimensions Are There? [Adam, 03/29/2001]
  How do we know how many dimensions there are? What is the significance of drawing 4D hypercubes? If I were in a 2D world, how would I be able to represent 3D objects?

• Tic-Tac-Toe on a Torus [Joe, 03/29/2001]
  Can you make a tic-tac-toe game that won't end in a tie?

• Planes between Planes [Nikila, 04/02/2001]
  How can I find if a plane lies between two other planes?

• Proof of Pappus' Theorem [Boersma, 04/02/2001]
  How can I prove Pappus' theorem of colinearity with the help of Menelaus' theory?

• Radius of a Tennis Ball [Goodsky, 04/03/2001]
  How can we find the radius of a tennis ball without cutting it open?

• Inclusive and Exclusive Definitions [Hawes, 04/05/2001]
  Are squares rectangles? Are rectangles squares?

• Area of Part of an Ellipse [Townsend, 04/07/2001]
  Given an ellipse with a line bisecting it perpendicular to either the major or minor axis of the ellipse, what is the formula for the area of the ellipse either above or below that line?

• Point and Line [Shiva, 04/07/2001]
  How does something without dimension create something with dimension?

• Euler's Line Theorem [Mahta, 04/08/2001]
  Prove that the circumcenter, orthocenter, and centroid of any triangle lie on the same line using analytical geometry.

• Maximum Difference, Longitude and Latitude [Mini, 04/10/2001]
  Find the maximum longitude and latitude difference between two points on Earth 1000 kilometers apart.

• Volume of Ellipsoidal Cap [Shanks, 04/11/2001]
  I am doing research on cancer and need a way to properly determine the volume of tumors in lab animals.

• Euclidean Formula for Orthogonal Circles [Alisen, 04/11/2001]
  When considering the case when circle C has center at the origin and radius 1, we need to show that the equation of the circle orthogonal to circle C and with center (h,k) is given by: x^2-2hx+y^2-2ky+1=0.

• Finding Area and Volume [Brandi, 04/12/2001]
  When working with area and volume of triangular shapes, how do I know when to divide the base by 2 and when to divide it by 3?

• Nagel Point [Max, 04/15/2001]
  What relation does the Nagel Point have to the incenter, centroid, and Spieker point of a triangle?

• Perimeter of a Reuleaux Triangle [Deborah, 04/15/2001]
  How can I find the perimeter of a Reuleaux triangle of width h?

• Line and Unit Circle; Pythagorean Triples [Kennedy, 04/16/2001]
  If (X,Y) is a point in the 1st quadrant on the unit circle and m is the slope of the line passing through (X,Y) and the point (0,-1), how can I express the coordinates (X,Y) in terms of m? Can this be used to generate Pythagorean triples?

• Golden Ratio and the Sine of 18 [David, 04/17/2001]
  2*sin(18) + 1 is equal to the golden ratio. Is there any significance to this?

• Parts of a Cone [Brian, 04/18/2001]
  Does a solid cone have any edges?

• How Tall is Hal? [Helen, 04/18/2001]
  Hal is standing 40 feet away from a 36-ft. tree. If the distance from the top of the tree to the top of Hal's head is 50 ft., how tall is Hal?

• Circle Tangent to Line [Lewis, 04/19/2001]
  Construct the circle that passes through two given points and is tangent to a line.

• Ellipse Area and Circumference [Sonja, 04/19/2001]
  How can I draw an ellipse and find the area and circumference?

• Triangle Proof: r + r1 + r2 = CD [Rebecca, 04/20/2001]
  Let CD be an altitude of triangle ABC, and assume that angle C = 90 degrees. Let r1 and r2 be the inradii of triangle CAD and triangle CBD, respectively, and show that r+r1+r2=CD, where r is the inradius of triangle ABC.

• Tesseract [Robert, 04/25/2001]
  Why does a tesseract contain eight cubes?

• Origami Equilateral Triangle [Oliver, 04/26/2001]
  How can I create an equilateral triangle from a piece of paper using only origami-like folds?

• Distance to the Corner of a Rectangle [Jay, 05/01/2001]
  How can I find the distance from a point P inside a rectangle to the fourth corner if the distance from P to one corner is 3, from P to the opposite corner is 5, and from P to a third corner is 4?

• Finding the Table's Diameter [Sarah, 05/05/2001]
  A circular table is pushed into the corner of a room so that it touches both walls. On the edge of the table is a scratch 8" from one wall and 9" from the other wall. What is the diameter of the table?

• Polygon Algorithms [Andriy, 05/10/2001]
  Given a polygon as a set of points (X, Y) and a database table with X and Y columns, select all records/points from the table that are inside the polygon or belong to its border.

• Inverse Pythagorean Theorem [Julie, 05/10/2001]
  How can you tell a triangle is a right triangle without looking at the triangle and just how long the sides are?

• Deriving Pi [Leslie, 05/10/2001]
  I know that Pi is equivalent to 3.14, but what formulas are used to come up with 3.14?

• Line Dividing a Plane [Jessica, 05/11/2001]
  Given a square (graphed on the Cartesian coordinate system) and a point in the square, draw a line through the point that will divide the square into two regions: one the smallest area possible, the other the largest possible.

• Radius of Circumscribed Circle [Peter, 05/11/2001]
  Where can I find a derivation of R = abc/4K?

• Sextant Theorem [Yolanda, 05/13/2001]
  What mathematical theorem is behind using a sextant, and can it be proved?

• Pentagon Area Using No Trig [Sandra, 05/14/2001]
  Where I am stumped is finding the area of one of the five triangles.

• Writing a Proof [Tony, 05/16/2001]
  Is there a certain way I should go about writing a proof?

• Pythagorean Theorem in Three Dimensions [Erin, 05/18/2001]
  Given a tetrahedron with a trirectangular vertex S. Let A, B, and C be the areas of the three faces that meet at S, and D be the area of the face opposite S. Prove that D^2 = A^2 + B^2 + C^2.

• Parabolas in Everyday Life [Ledesma, 05/18/2001]
  What types of things have been made using parabola shapes?

• Five Equal Pieces of a Square Cake [Katie, 05/22/2001]
  Ravina wants to cut a square cake using straight vertical cuts to make five pieces of equal volume. If she makes the first cut from the cake's center to the top left corner, where must she make the other cuts if they all start from the cake's center?

• Measuring by Shadows [RioBranco, 05/22/2001]
  How can I measure a tree using its shadow and mine?

• Surface Area and Volume of Cylinders [Gibbs, 05/25/2001]
  How do you find the surface area and volume of a cylinder?

• Importance of Surface Area [Francine, 05/26/2001]
  Why is surface area so important? What kinds of things depend on surface area?

• Grazing Areas [Siddharth, 05/29/2001]
  Find the total area grazed by three horses.

• Goat and Silo [David, 05/31/2001]
  A goat is roped to a point A next to a silo 30 ft. in diameter. The rope is 15pi feet long. How much area can goat graze?

• Sizing a Connector [Tom, 06/01/2001]
  I have to come up with a specific diameter for anywhere from 2 to 91 diameters that are bunched together. The application is round wires.

• Numerically Equal Volumes and Surface Areas [Irene, 06/04/2001]
  Find all rectangular solids with integral dimensions, the volumes and surface areas of which are numerically equal.

• Parabola [Adam, 06/06/2001]
  What is the meaning of the word parabola?

• Simson Lines [Gabriel, 06/07/2001]
  Show that, given two triangles inscribed in the same circle, for any point P on the circle the two Simson's lines form a fixed angle.

• Euler's Formula Applied to a Torus [Jim, 06/08/2001]
  Can you explain why Euler's characteristic is zero for a torus?

• Finding Points on the Earth [Ryan, 06/08/2001]
  Find the point that has latitude and longitude five miles north of a given point, and the other three points to the south, east, and west.

• Foci of an Ellipse [Scott, 06/08/2001]
  If the major and minor axis of an ellipse are given, how do I find the focus points?

• Proof Using Coordinate Geometry [Andrew, 06/08/2001]
  In equilateral triangle ABC, a segment is drawn from point A to the side BC at a point (D)... prove that angle BFC (or EFC) is a right angle.

• Area of Bermuda Triangle [Bronwyn, 06/10/2001]
  The Bermuda triangle is shown on a graph with the points A(1,2) B(4,8) and C(8,1). Determine the area of the triangle two different ways.

• Beyond Three-Dimensional Geometry [Tanner, 06/17/2001]
  If the first dimension is a line and the second dimension is a flat figure, the the third dimension is, say, a cube, then what is the fourth dimension? What is the fifth dimension?

• Find the Cities [Rod, 06/19/2001]
  Given the latitudes and longitudes of Detroit, MI, and Miami, FL, find every city within 10 miles of a straight line between them.

• Endpoint of an Arc [Bryson, 06/25/2001]
  Given the center of the circle, the angle of the arc, the radius of the circle, and the starting point of the arc, determine the end point of the arc using cartesian coordinates.

• A Three-Legged Stool [Teri, 06/26/2001]
  Why is a three-legged stool steady, while a four-legged stool can be wobbly?

• Minimum Angle Proof [Pieta, 07/05/2001]
  Label the point of intersection of the angle bisectors of triangle ABC as Q. Let M be the midpoint of side BC. Given that MQ = QA, find the minimum value of angle MQA.

• Swimming Pool Volume [Jim, 07/26/2001]
  How many gallons will an above-ground 24-foot-diameter pool 48 inches tall hold?

• Dividing a Square Cake into Five Equal Pieces [Pam, 07/28/2001]
  How can you divide a square-topped cake that is a rectangular solid and is frosted on all faces into five pieces so that everyone receives the same amount of cake and icing?

• 16-sided Regular Polygon [Tiffany, 07/31/2001]
  How can I construct a 16-sided polygon?

• Sum of Angles of a Triangle in Non-Euclidean Geometry [Roger, 08/01/2001]
  In a triangle on the surface of a sphere the sum of the angles is not 180 degrees. Is that possible? Why?

• Cross-Section of a Prism [Shaun, 08/02/2001]
  Please define cross section, and explain the formula for the volume of a prism.

• Obtaining Bearing from a Velocity Vector [Michael, 08/01/2001]
  I have the x, y, and z components of a velocity vector of an airplane, and must use this vector to calculate the bearing of the plane.

• Point Inside or Outside Triangle? [Natalie, 08/02/2001]
  I have coordinates of three vertices of the triangle and coordinates of the point.

• Dividing a Cylinder [Jon, 08/06/2001]
  How can I divide a cylinder that is 4 by 9 inches into two smaller cylinders, each with the same volume?

• Tiling with Dominoes [Ethan, 08/06/2001]
  A 6-square by 6-square board is tiled completely with 18 2x1 dominoes. Prove that at least one horizontal or vertical line can be drawn along the edges of the dominoes that divides the board into 2 regions, without cutting any dominoes in half.

• Perimeter of a Right Triangle [Hanul, 08/14/2001]
  What is the perimeter of a right triangle with hypotenuse 65 that can be circumscribed about a circle with radius 12?

• Point Symmetry [Tammy, 08/19/2001]
  What exactly is point symmetry? How can one tell if point symmetry is present?

• Surface Area of a Right Cylinder [Ramonda, 08/21/2001]
  The problem in my book asked me to find the surface area of a right cylinder in centimeters with the dimensions given in meters.

• Sphere Equation Variables [Timmy, 08/21/2001]
  In the standard equation: r^2 = (x-h)^2 + (y-K0^2 + (z-l)^2 ...what do the points h, k, and l represent?

• Calculating the Angle of a Plank [Nick, 08/22/2001]
  Are there any equations that could be used to solve for a plank of known width?

• Octagon Side Lengths [Rob, 08/22/2001]
  If I know that the dimension of an octagon from one side to the other is 8 feet, how can I find the lengths of a side?

• Equable Shapes: Triangle [Natalie, 08/27/2001]
  I have been asked to do a piece of coursework on equable shapes, but I am stuck on the triangle.

• Finding Angles without Using Trigonometry [Marc, 08/27/2001]
  Given the lengths of three sides of a triangle, determine the measures of the three angles using only geometry and algebra.

• Construct a Trapezoid [Sarah, 08/28/2001]
  I tried drawing two lines that are parallel to each other for b and f, and I drew c, but then d didn't fit. How do I construct this?

• Order of a 3D Triangle [Vincent, 08/29/2001]
  If I visit the vertices of a 3D triangle in order going from a to b to c, am I going clockwise or anticlockwise?

• Determining the Length of a Coil of Ribbon [George, 08/31/2001]
  How will calculus give me the same answer I found with algebra and geometry?

• Cone Frustum [Mitch, 08/31/2001]
  I am trying to calculate the height of a right frustum cone knowing only r, V, and the angle of the side.

• Dimensions [Emily, 08/30/2001]
  What are 1-dimensional, 2-dimensional, and 3-dimensional? What's the difference?

• Dividing a Circle using Six Lines [Jordy, 08/29/2001]
  What is the largest number of regions into which you can divide a circle using six lines?

• Grazing Half of a Square Field [Philip, 08/30/2001]
  My cow is tied to the middle of one side of a SQUARE field. What is the length the rope should be to enable the cow to eat half the grass?

• Segment of an Ellipse [Martin, 09/06/2001]
  We often use horizontal oval tanks for storing drinking water and fuel, and we would like to be able to calculate the contents.

• Converse, Inverse, Contrapositive [Hana, 09/08/2001]
  Write the converse, inverse, and contrapositive of each conditional and determine whether they are true or false; if false, give a counterexample.

• Triangle Construction [Becca, 09/09/2001]
  Given a triangle ABC and point D somewhere on the triangle (not a midpoint or vertex), construct a line that bisects the area.

• Union of Spherical Caps [Phil, 09/10/2001]
  Suppose I have two spheres of radius r1 and r2 respectively, and they partly overlap. What's the formula for the overlapping volume?

• Surface Area of Blocks Glued Together [Jodi, 09/09/2001]
  Three cubes whose edges are 2, 6, and 8 centimeters long are glued together at their faces. Compute the minimum surface area possible for the resulting figure.

• Equal Area and Perimeter: Rectangles [Jessica, 09/09/2001]
  There are only two rectangles whose area is exactly the same as their perimeter if the dimensions of each are whole numbers. What are the dimensions?

• How Many Rectangular Solids in a Cube? [Right, 09/13/2001]
  Is there any standard way of finding out how many different possible rectangular solids can fit into an 3^3 cube?

• Height of Tetrahedral Pyramid [Bob, 09/12/2001]
  I'm looking for a simple formula (and derivation) of the height of a tetrahedral pyramid with an equilateral triangle as a base.

• Circles in a Square [Ash, 09/15/2001]
  A circle of radius 1 is inside a square whose side has length 2. Show that the area of the largest circle that can be inscribed between the circle and the square is (pi(17 - 12sqrt(2))).

• Short History of Geometry [Jason, 09/15/2001]
  Were there any people who helped to develop geometry besides Euclid?

• Why Proofs? Definitions and Axioms [Allie, 09/16/2001]
  Why are proofs important in the development of a mathematical system like geometry?

• Slope of Tangent to an Ellipse [Libby, 09/21/2001]
  If I know a point on an ellipse, how do I find the angle of the ellipse at that point?

• Symmetry Proof [Jane, 09/27/2001]
  Given an angle with vertex O and a point P inside the angle, drop perpendiculars PA, PB to the two sides of the angle, draw AB, and drop perpendiculars OC, PD to line AB. Then show that AC=BD.

• Equilateral Triangle - Centroid/Incenter [Casey, 09/27/2001]
  Prove that if a triangle is equilateral, its centroid coincides with its incenter, and vice versa.

• Degrees in a Sphere? Steradians [Caleigh, 09/27/2001]
  If one can say that a circle contains 360 degrees, how many degrees can one say are in a sphere?

• Instruments for Measuring Angles [Gentry, 09/28/2001]
  I need the name, picture, or description of five devices used to measure angles.

• Find Circle Center and Radius [Alex, 09/21/2001]
  Given three sets of (x,y) coordinates that lie on the circumference of a circle, how do you find the center and radius of the circle?

• Lattice Points on Hypotenuse [Alex, 10/01/2001]
  What is the number of lattice points on the hypotenuse of a right triangle?

• Volume of a Right Circular Cone [Jeffrey, 10/07/2001]
  Using calculus, derive the formula for the volume of a right circular cone with a radius of r and height h.

• Latitude and Longitude of a Point Halfway between Two Points [Chuck, 10/10/2001]
  I would like to know how to determine the latitude and longitude of a point halfway between New York and Los Angeles.

• Circumference of a Tube [Ernie, 10/11/2001]
  What effect does the thickness of a tube have on the circumference when it's formed into a circle?

• Arbelos Construction [Mark, 03/10/2000]
  Is there a Euclidean construction for the circles that are sandwiched in the Arbelos?

• Hypercube [Bruce, 10/13/2001]
  Have there been any recent developments in studying the fourth dimension?

• Area of an Annulus [Cindy, 10/13/2001]
  How can I find the area of an annulus?

• Carpet Problem [Nathan, 10/15/2001]
  You have to carpet a 9x12 room, but when you go the store they only have a 10x10 carpet and a 1x8 piece of carpet...

• Precision in Measurement: Perfect Protractor? [Ivan, 10/16/2001]
  Given that protractors are expected to be accurate to the degree, and in some instances the minute or second, how are angles accurately constructed and marked?

• Angle Trisection: Construction vs. Drawing [Joe, 10/17/2001]
  Has anyone ever divided an angle into three equal parts by construction? I have been told it has not been accomplished.

• Path Length or Displacement? [Corrie, 10/17/2001]
  A body moves from A due east 5m to B, then from B due north 6m to C, and from C due west 5m to D. Calculate total distance covered from A to D.

• Difference between Oval and Ellipse [Tarab, 10/18/2001]
  What is the difference between an oval and an ellipse? Am I right if I say that "all ellipses are ovals, but all ovals cannot be ellipses"?

• Moebius Strips: How Many Sides and Surfaces? [Melissa, 10/18/2001]
  What is the difference between a side and a surface?

• Measuring 3D Curvatures and Angles [Evan, 10/21/2001]
  What are solid angles and how are they measured? How and in what units can we determine the curvature of a sphere? What is the relation between solid angles and the spherical curves they create when they intersect a sphere whose center is the same as the vertex?

• Finding the Dimensions of a Box [Kaila, 10/21/2001]
  You want to construct a cardboard box from a cardboard strip that is 8 inches wide. The dimensions of the box are 8"x8"x4". How long does the strip need to be?

• World War II Window Blackout [Heron, 10/21/2001]
  Mr. Brown had a square window 120cm x 120cm, but the only material he could find was a sheet of plywood 160cm x 90cm; same area, different shape. He drew some lines and cut out just two congruent shapes, which he joined to make a square of the correct size. How did he do it?

• Non-Euclidean Geometry [Yj, 10/22/2001]
  What is non-Euclidean geometry? What two concepts are different from Euclidean geometry?

• Etymologies of Algebra, Geometry, Trigonometry [Nikki, 10/22/2001]
  What are the origins and roots of the words geometry, algebra, and trigonometry?

• Covering Paper using Index Cards [Liz, 10/24/2001]
  What is the maximum area of an 8"x13" sheet of paper that you can cover by using seven 3"x5" standard index cards?

• Maximum Rectangle within a Quadrilateral [Christophe, 10/25/2001]
  I need to extract from a quadrilateral the maximum area rectangle inside it.

• Carpet and Room Areas [Matt, 10/26/2001]
  A man buys a roll of carpet 9 ft. wide by 12 ft. long to fit a 10ft. by 10 ft. room. When the roll of carpet is unrolled, a hole is discovered in the middle of the carpet...

• Building a Cone [Gary, 10/28/2001]
  I am trying to find a formula for building a cone for a chimney flashing. It should be 21" tall with a top opening of 8", a bottom opening of 20", and a vertical seam overlap of 2".

• Degenerate/Nondegenerate Figure [Jan, 10/27/2001]
  We need to know what a nondegenerate circle is. (We're trying to decide whether this is a model of incidence geometry, but don't know the definition.)

• Equable Polygons [Liz, 10/29/2001]
  I need a formula for finding equable polygons. I know the formula 4/ tan(90-180/n), but how do you get to this point?

• Volume of the Frustum of a Pyramid [Kerry, 10/31/2001]
  I am trying to figure out how to derive the formula for the volume of a frustum of a pyramid.

• Equable Polygons and the Area of a Circle [Suzi, 10/30/2001]
  I have found a general formula to work out the side length a polygon (of any shape) must have to be equable, which is closely linked to finding an equation for the area of a circle without using pi (and therefore proving pi)...

• Interior and Exterior Angles [Kim, 10/19/2001]
  How can the sum of the angles in my quadrilateral be 280 degrees?

• Etymology of the Word Tessellation [Cindy, 11/05/2001]
  Are tessellations related to the tesseract in Madeleine L'Engle's _Wrinkle in Time_ series?

• Equilateral Triangle Proof [Chenelle, 11/05/2001]
  Let a, b, and c be the lengths of the sides of a triangle. Show that if a*a + b*b + c*c = bc + ca + ab, the triangle is equilateral.

• Circle Overlap [Justin, 11/08/2001]
  Circle A and Circle B both have a radius of 1 unit. The centers of each circle are 1 unit apart as well. Find the area of the union of the two circles.

• Meaning of '-ominoe' [Bunker, 11/07/2001]
  We are drawing pictures of dominoes, triominoes, tetrominoes, and pentominoes. What is the meaning of the root "ominoe"?

• Radian to Degree Conversions [Jason, 11/11/2001]
  Can you give me a table of radian measures and their reference degree measures for the unit circle?

• Circles of More than 360 Degrees [Benn, 11/10/2001]
  What shape is formed if one cuts along the radius of a circle and adds degrees by adding a sector?

• How Many Congruent Triangles? [Sally, 11/11/2001]
  Given a scalene triangle and a point P on some line L, how many triangles are there with one vertex at P, another vertex on L, and each triangle congruent to the given triangle?

• Euler Line Proof [Natalie, 11/13/2001]
  Prove that if the Euler line of a triangle passes through a vertex, then the triangle is either right or isosceles.

• Incenter Equidistant from Sides of Triangle [April, 11/18/2001]
  Prove that the point of intersection of the angle bisectors of a triangle is equidistant from the sides of the triangle.

• Sine of 36 Degrees [Steven, 11/18/2001]
  Ptolemy calculated the sine of 36 degrees geometrically using the construction of a regular pentagon. How did he do it?

• Copies of U.S. on Surface of Earth [Nathan, 11/07/2001]
  I need to determine the number of identical copies of the continental United States that would fit on the surface of the Earth.

• Optical Illusions and Math [Elizabeth, 11/20/2001]
  How are optical illusions related to mathematics?

• Proof for Volume of a Segment of a Sphere [Shelaine, 11/19/2001]
  I am in need of assistance in proving the volume of a truncated spherical cap (or a segment of a sphere I think it is also called).

• Triangle Proof [Ashley, 11/19/2001]
  Mapping out a general method for proceeding with proofs.

• Kitchen Tabletop [Russell, 11/21/2001]
  I need to determine the correct pivot point...

• Fibonacci Riddle [Daniel, 11/21/2001]
  We can cut an 8x8 square with an area of 64 into four pieces and reassemble to get a 5x13 rectangle with an area of 65. Where does the extra 1x1 square come from?

• Planes Intersecting Space [Gafur, 11/24/2001]
  Can we say that n planes divide space into at most 2^n regions?

• Diameter of a Ball [Tabitha, 11/25/2001]
  A child rolls a ball on a level floor 4.5m to another child. If the ball makes 15 revolutions, what is its diameter?

• The Incenter and Euler's Line [Madison, 11/27/2001]
  Why is the incenter of a triangle not on the Euler line?

• Why Cubed? [Bob, 11/27/2001]
  Why do we use "cubed" for the volume of a figure?

• Indirect Proof of Parallel Lines [Ryan, 11/26/2001]
  I have asked my high school geometry class to prove indirectly that parallel lines have the same slope. Unfortunately, I cannot figure out how to do it myself...

• What is Dimensional Analysis? [Danielle, 11/26/2001]
  What is dimensional analysis and how does it work?

• Goat Tied by a 10-Meter Rope [Sadia, 11/28/2001]
  A goat is tied to the corner of a 5-by-4-meter shed by a 10-meter rope. What area is grazed by the goat? If the shed is a circle with radius r, and the rope is 2r, what is the area grazed?

• Congruent Parts Congruent Triangles Congruent (CPCTC) [Brittany, 11/28/2001]
  When should we use CPCTC, and how does it prove anything?

• Mapping a Sphere to a Plane [Candice, 11/28/2001]
  Maps of the world are always distorted in some way when put on a flat map instead of a globe. Why?

• Euler's Formula [Amanda, 11/26/2001]
  I have to find Euler's formula for two-dimensional figures and explain it at a university level and at an elementary-school level.

• What is a Property? [Jim, 11/29/2001]
  I understand Undefined and Defined terms and Axioms and Theorems, but what exactly is a Property? Is it the same thing as a Theorem? Also what is a Law?

• Regular Pentagon Construction Proof [Joe, 11/23/2001]
  What is the proof of the construction of a regular pentagon?

• Longest Ladder [Michelle, 11/30/2001]
  Two hallways, one 8 ft. wide and other 4 ft. wide, meet to form a right angle. What is the longest ladder that can go around the corner where the hallways meet?

• Proving Quadrilateral is a Parallelogram [Kara, 11/30/2001]
  We are having a problem with the idea of a quadrilateral having one pair of opposite sides congruent and one pair of opposite angles congruent.

• Area of an Oval [Colin, 11/30/2001]
  How do I figure out the area of an oval 17" x 38"?

• Construct Polygon Given One Side [Dieter, 12/03/2001]
  How can you construct a polygon, given one side?

• Building a Manger [Anne, 12/03/2001]
  Given a base of 11" and two walls 7 1/2' and 6" high, both meeting the base a 90-degree angles, what is the length of the roof and what are the angle measures where the walls meet the roof?

• Find the Fourth Side [Suzy, 12/03/2001]
  The successive sides of a quadrilateral are 2, 6, 9, and x. If the diagonals of the quadrilateral are perpendicular, compute x.

• Bases and Faces [Madison, 12/05/2001]
  I can't figure out the difference between a base and a face on the shapes we are learning.

• Area and Perimeter: Isoperimetric Quotient [Ace, 12/05/2001]
  What is the isoperimetric quotient of a two-dimensional shape? Is it a measure of compression?

• Cups and Volume [Kedra, 12/06/2001]
  How can I calculate the volume of a box, if I know how many cups of rice fill it? And how can 2 cups be a volume measure?

• Latitude and Longitude, GPS Conversion [MS, 12/07/2001]
  What is the equation to convert latitude/longitude/altitude (LLA) data into earth-centered/earth-fixed (ECEF) data?

• Equilateral, Isosceles, Scalene - Word Origins [Julian, 12/09/2001]
  I need to find out about the origins of the scalene, isoceles, and equilateral triangles. How they were named?

• Distances from a Point inside an Equilateral Triangle [Russ, 12/09/2001]
  Prove that the sum of the distances from a point inside an equilateral triangle, measured parallel to the sides, is equal to the length of the side of the triangle.

• More on Geometry Proofs [Cherie, 12/11/2001]
  I don't understand how to get from the given to the prove part. All the statements sound the same.

• Oil Can Dimensions [Shannon, 12/11/2001]
  What are the dimensions of an oil can with a one-liter capacity that uses the least amount of tin?

• Triangle Construction Given Medians [Chandra, 12/12/2001]
  Given median lengths 5, 6, and 7, construct a triangle.

• Line or Ray Longer? [Leslie, 12/11/2001]
  Which is longer, a ray or a line?

• Visible/Hidden Sides on Stacked Cubes [Robin, 12/12/2001]
  Find a formula for the number of sides hidden/visible on cubes when put in different arrangements: a line; a double line; stacked three- dimensionally.

• Non-Congruent Triangles [Z, 12/12/2001]
  Construct and prove that there can be two non-congruent triangles in which five parts of one triangle are equal to five parts of another.

• Maximum Area of Inscribed Triangle [Shawn, 12/10/2001]
  An isosceles triangle is inscribed in a circle of radius R. Find the value of Theta that maximizes the area of the triangle.

• Theorem of the Broken Chord [James, 12/14/2001]
  Prove the theorem of the broken chord (if AB and BC make up a broken chord in a circle, where BC is greater than AB, and if M is the midpoint of arc ABC, the foot F of the perpendicular from M on BC is the midpoint of the broken chord).

• Sum of Star Angles [Jake, 12/19/2001]
  Find the sum of the measure of the angles formed at the tips of each star irregular star.

• Proving Trapezoid Congruency [Peter, 12/19/2001]
  Prove that the sides of a trapezoid are congruent if the diagonals of the trapezoid are congruent.

• Bearing between Two Points [Doug, 12/19/2001]
  Is there an easy way to calculate the "heading" (relative to North=0) between two coordinates?

• Equation of a Parabola [Richard, 12/20/2001]
  Given several points that appear to be a parabola, how do you approximate the equation that would give a similar graph?

• Remembering Area Formulas [Summer, 12/23/2001]
  Is there was a good way to help me memorize the formulas for areas of different shapes?

• Finding Line Segment Lengths [Annie, 12/21/2001]
  Can you help me find line segments AB and BC if points A,B,C, and D are collinear with B between A and C and C between B and D...?

• Volume of Partially Full Cylinder on its Side [Charlie, 12/31/2001]
  I am in charge of ordering fuel for our company, and the way the owner calculates the volume is via a grossly simplified percent full guesstimation...

• Transformation between (x,y) and (longitude, latitude) [Hing, 01/02/2002]
  I have two questions on the transformation between (x,y) and (longitude, latitude).

• Small Section of a Sphere [Sph, 01/10/2002]
  Find the volume and the areas of each of the surfaces/faces of a small section of a sphere with "dimensions" delta r, delta theta, delta phi, in spherical coordinates.

• Intersection of Circles [Peter, 01/16/2002]
  Given two intersecting circles, find the coordinates of the intersection point(s).

• Volume of Tacoma Dome [Kacey, 01/16/2002]
  I am trying to figure the volume of the Tacoma Dome in Tacoma, Washington.

• Cyclic Trapezoid [Varghese, 01/17/2002]
  PQ is a diameter; AB is a chord parallel to PQ. If PQ=50cm and AB= 14cm, find PB.

• Centroid, Circumcenter, Incenter, Orthocenter: Etymologies [Meghan, 01/20/2002]
  Why are the points centroid, circumcenter, orthocenter, and incenter named as they are, and are there any other special points associated with triangles?

• SSS, ASA, SAS Proofs [Sarah, 01/21/2002]
  I understand the ideas, but I'm not sure when and where to use them.

• Unit Sphere [Jordan, 01/21/2002]
  Is there such thing as a "unit sphere" that has to do with trigonomic functions and the placement of points on said sphere?

• Collapsible Compass [Shane, 01/23/2002]
  How did the early Greek mathematicians reproduce lengths with a collapsible compass?

• Rule of Three [Roger, 01/23/2002]
  How high above the surface of the earth must a person be raised to see 1/3 (one third) of its surface?

• Isosceles Trapezoid Proof [Ana, 01/18/2002]
  Given: ABCD is an isosceles trapezoid with bases BC and AD. Prove: ABCD is an isosceles trapzoid.

• Parabolic Golf Shot Equations [Michelle, 01/24/2002]
  Does the ball reach the green?

• Triangle Area Proofs [Joshi, 01/23/2002]
  An analytic proof.

• Finding a Missing Angle [Mel, 01/23/2002]
  Using trigonometry, calculate the measure of angles ABC and ACB.

• Volume of a Tetrahedron [Andrew, 01/23/2002]
  The volume of a tetrahedron is one-third the distance from a vertex to the opposite face, times the area of that face. Find a formula for the volume of a tetrahedron in terms of the coordinates of its vertices P, Q, R, and S.

• Is Geometry a Language? [Jordan, 01/28/2002]
  I have to write an essay to defend or criticize the statement, "Geometry is a Language."

• Building a Cone [Surendra, 01/28/2002]
  I am trying to draw cone (frustum) with a larger radius size.

• Volume of Spherical Cap [Roger, 01/29/2002]
  If a heavy sphere, whose diameter is 4 inches, be put into a conical glass full of water whose diameter is 5 and altitude 6 inches, how much water will run over? Ans: nearly 35/47 of a pint.

• Light Beam Reflection [Teri, 01/31/2002]
  Four mirrors form a rectangle 3 m by 2 m. A light beam is shone from A at 45 degrees. Which corner does the beam strike first?

• What Fraction of Water Overflows? [Asim, 02/04/2002]
  A conical vessel of radius 6cm and height 8cm is completely filled with water. A sphere is lowered into it and its size is such that when it touches the sides of the conical vessel it is JUST immersed. What fraction of water overflows?

• Woodworking Curve [Tony, 02/06/2002]
  I am making a cabinet and I want to put a curve on the front of the shelves. The "chord" of the circle would be 15" and a perpendicular line from the center point of the chord to the circumference of the circle is 1".

• Volume of a Cone [Henry, 02/08/2002]
  I have observed that a cone consists of a right triangle and a circle base, and I have came up with another method of calculating the volume of a cone...

• Area of a Right Triangle [Chris, 02/09/2002]
  Find the area of a right triangle that has a perimeter of length 16 meters and a hypotenuse with length 7 meters.

• Rectangles on a Chessboard [Dave, 02/09/2002]
  How many rectangles are there on a chessboard?

• Height of a Trapezoid [Sam, 02/08/2002]
  A trapezoid has parallel bases of lengths 5 and 30, and non-parallel sides of length 5 and 25. Find the height of the trapezoid.

• Area of a Circle with Radius less than 1 [Kelly, 02/18/2002]
  If the radius is less than 1 it just gets smaller and you get a smaller area...

• Frustum of a Pyramid with a Rectangular Base [Brad, 02/20/2002]
  I am an engineer with a water treatment agency and need to figure the amount of water per foot of elevation in our reservoirs...

• Octagon Construction Using Compass Only [Janci, 02/22/2002]
  Construct the vertices of a regular octagon using just a compass. The only thing you know about the octagon is the circumradius.

• Floating Copper Ball [Amber, 02/26/2002]
  Find the wall thickness of a hollow copper ball (sphere) with an outside radius of 50.0 cm that "just floats" in water.

• Do Pyramids Really Exist? [Joeli, 02/27/2002]
  If the base of an isosceles triangle is 4, and the height is 5, then the sides are equal to the square root of 21. How can this triangle exist (except in theory) if you can never measure or draw the square root of 21?

• Why Learn Geometric Proofs? [Sarah, 02/27/2002]
  Why are we taught geometric proofs if the vast majority of us will never use them?

• Squares and Circles: How Many Intersections? [Ashley, 02/27/2002]
  What is the largest possible number of times a square can intersect a circle when the square is placed on top?

• Swimming Pool Volume [David, 02/28/2002]
  What formula would I use to calculate the volume in gallons of a swimming pool 135' x 70' with different depths of 3', 5', 8' and 11'?

• What is Geometry For? [Sum, 03/01/2002]
  What is geometry really for?

• Trapezoid Diagonals and Midpoints of Parallel Sides [Leonard, 03/04/2002]
  In a trapezoid, why are the midpoints of the parallel sides collinear with the intersection of the diagonals?

• Side Length of a 17-gon [Jenny, 03/03/2002]
  Given a 17-gon inscribed in a circle of radius 1, what is the length of a side to 6 decimals?

• Three Pyramids in a Cube [Chaitu, 03/04/2002]
  How can three pyramids fit exactly into a rectangular prism?

• Completing the Square Using a Diagram [Kelvon, 03/06/2002]
  Show x^2 + 3x using a diagram.

• Finding Miles Per Hour [Joshua, 03/06/2002]
  If a wheel is making 64.2 revolutions per minute, how many miles per hour is it going?

• Cubes in a Big Cube [Yannik, 03/11/2002]
  Is there a formula for the number of cubes in an n*n*n cube?

• Isoperimetric Quotient [Andreas, 03/11/2002]
  Is there an equation for the ratio of surface area to volume?

• Volume of a Conical Wedge [Roger, 03/04/2002]
  Two porters agree to drink off a quart of strong beer between them, at two pulls, or a draught each...

• Triangle Construction [Louise, 03/11/2002]
  Let ABC be a triangle with sides a, b, c. Let r be the radius of the incircle and R the radius of the circumcircle. Knowing a, R, and r, onstruct the triangle using only ruler and compass.

• Finding Where Planets are Rising/Setting [Robert, 03/12/2002]
  Find a formula that calculates where (in longitude and latitude) the different celestial bodies are on the horizon, either setting or rising.

• Parabolas, -b/2a ? [TJ, 03/13/2002]
  I've thought about why the form -b/2a works when trying to graph a parabola, but I just cannot figure it out.

• Triangle Construction Given Two Angles and Semiperimeter [Keeley, 03/14/2002]
  Given two angles, A and B, and the semiperimeter, construct the triangle.

• Getting Started with Two-Column Proofs [Kayla, 03/19/2002]
  Write a two-column proof: If the altitude is drawn from the vertex of the right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and to each other.

• Degrees and Radians, Explained [Mandy, 03/19/2002]
  How do you find the degree measure for an angle from pi/60 rad?

• Grad as a Measure of an Angle [Evelyn, 03/20/2002]
  I would like to know about the origins, use in the past, and whether (and how) the grad is used now.

• Secant-Tangent Theorem [Jon, 03/21/2002]
  I'm trying to prove the secant-tangent theorem.

• Perimeter of a Strange Figure [Kayleigh, 03/23/2002]
  I don't understand how to find the area or perimeter of a shape that looks like a rectangle with a small triangle to the left on top...

• Centroid - Center of Gravity [Jack, 03/25/2002]
  Can a triangle have a unique centre of gravity?

• Parabola Given Three Points [Samuel, 03/27/2002]
  How can I find the equation for a parabola given three points on it?

• Triangle Construction Given an Angle, the Inradius, and the Semiperimeter [Tiffany, 03/26/2002]
  Given an angle, alpha, the inradius (r), and the semi-perimeter (s), contruct the triangle.

• Describe the Locus [Andrea, 03/28/2002]
  What is the locus of all points in a plane two inches from a point A?

• Pythagorean Theorem Proof (Thabit ibn Qurra) [Natalie, 03/28/2002]
  Proving a series of congruent triangles.

• Proving Lines Congruent [Allison, 03/29/2002]
  Prove line AL is congruent to line CM.

• Common Internal Tangent [Naveed, 03/29/2002]
  Two circles with radii 9 and 6 are 2 cm. apart. Find the length of the common internal tangent.

• Is Kite the True Name? [Beecky, 03/29/2002]
  Is kite the true math name for this shape, or is there another?

• One Degree Latitude, Longitude: How Many Miles? [Nick, 04/02/2002]
  Approximately how many miles are there in one degree of longitude and one degree of latitude in the states of Kansas and Oklahoma?

• Leg of a Triangle [Lucy, 04/02/2002]
  I need to know where the name "leg" of a triangle comes from, or what its origin is.

• Inscribing a Square within a Half-Circle [Michael, 04/05/2002]
  Is there a way to inscribe a square within a given half-circle?

• The Second Octant [Kjetil, 04/03/2002]
  Where is the second octant? No one seems to know how to count the next octants after the first.