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?