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Dr. Math FAQ:
Browse High School Euclidean/Plane Geometry
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Pythagorean theorem proofs.
- Finding the Center of a Circle [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.
- Finding the Length of a Coil [07/07/1999]
How can I find the length of a coil or spring given the diameter and
pitch and number of turns?
- Finding the Radial Separation of a CD Track Spiral [10/04/2000]
On audio CDs a track of pits spirals outward from a radius of 25 mm to a
radius of 58 mm. How can I calculate the radial separation of the pits?
- Find the Perimeter of the Fence [02/19/2003]
A convex polygon with perimeter P has a fence around it. The distance
from the polygon to the fence is 1m. How long is the fence?
- Find the Perimeter of the Rectangle [09/06/2002]
Two circles of radii 9 and 17 centimetres are enclosed within a
rectangle with one side of length 50 cm. The two circles touch each
other, and each touches two adjacent sides of the rectangle. Find the
perimeter of the rectangle.
- Find the Radius of the Circles [11/03/2002]
Given a 3,4,5 triangle, and inside it, inscribed, two circles of equal
radii. Both circles touch one leg and the hypotenuse, and both are
tangent to each other at one point. Find the radius of the circles.
- Finite vs. Infinite [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?
- Fitting a Picture to a Frame [11/14/1996]
I have a picture frame that needs to have twice as much border on the
side of the picture as on the top. If the photo is half the area of the
frame, how wide should the borders be?
- Five Noncollinear Points [4/2/1995]
In general, how many undirected lines and how many circles are
determined by five noncollinear points?
- Foil Wrapped Around a Spindle [12/17/1997]
I have a problem in an engineering work environment. I need to know the
length of foil (L) needed to generate the external diameter...
- Folium of Descartes and Parametric Equations [11/23/1998]
How do you plot an implicit function, such as the folium of Descartes,
with the equation y^3 + x^3 = 3xy?
- Formula for Factors of a Number [11/3/1996]
How many triangles can you draw on a square grid of dots of size x*x?
- Formula for Radial Latitudes and Longitudes [10/15/2002]
I want to make a radius search tool that returns all places based on
latitude/longitude within a certain radius of a given place.
- Geometric Probability [5/1/1996]
What's the probability of an asteroid hitting the earth?
- Geometric Proofs [11/28/1998]
I am tring to help a friend learn geometric proofs. Do you have any
- Geometry Class [9/2/1996]
How can I survive my first year of high school geometry?
- Geometry for Police Officers [02/24/1997]
How is geometry ever going to help me in my career as a police officer?
- Geometry of a Bicycle [11/30/1997]
How do you show everything geometrical about a bicycle?
- Geometry - Parallel Lines [12/09/1997]
Given: EJ = EK; JK||MN; Prove: Angle M = Angle N.
- Geometry Proofs: Lines and Planes [11/08/1998]
Show that two intersecting lines intersect in exactly one point...
- Geometry Proof - The Inscribed Angle is 1/2 of the Central Angle [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?
- Geometry Unit on Quilting [07/16/1997]
Do you have any information/units/lessons/curriculum ideas on quilting in
- Geometry vs. Trigonometry [07/14/1997]
What is the difference between trigonometry and geometry?
- Getting Started with Two-Column Proofs [03/19/2002]
Write a two-column proof: If the altitude is drawn from the vertex of the
right triangle to its hypotenuse, then the two triangles formed are
similar to the given triangle and to each other.
- Goat and Silo [05/31/2001]
A goat is roped to a point A next to a silo 30 ft. in diameter. The rope
is 15pi feet long. How much area can goat graze?
- The Goat In the Field Problem [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?
- Goat on a Rope [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?
- Goat Tied by a 10-Meter Rope [11/28/2001]
A goat is tied to the corner of a 5-by-4-meter shed by a 10-meter rope.
What area is grazed by the goat? If the shed is a circle with radius r,
and the rope is 2r, what is the area grazed?
- Goat tied to a barn [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.
- Golden Spiral [03/23/1998]
What is the equation of the Golden Spiral?
- Grad as a Measure of an Angle [03/20/2002]
I would like to know about the origins, use in the past, and whether (and
how) the grad is used now.
- Hose Length [07/11/1999]
Find the length of a 1" OD hose that is wrapped around a 10-inch cylinder
- How Can a Line Have Length? [04/14/1998]
If a Euclidean point has no length, how can a union of Euclidean points
form a Euclidean line segment with length?
- How Many Acute Angles from Three Intersecting Lines? [10/14/2002]
What is the greatest number of acute angles you can make with three
- How Much Carpet is Left? [03/27/1999]
We use rolled carpet in our business and would like to know how much is
left on a roll given the remaining diameter...
- How Much Does a Beam Bulge When it Expands? [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?
- How Much Material to Purchase? [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...
- How to Build a Proof [05/18/1999]
Given: Triangle ABC is a right triangle... Prove: Angle A and angle B are
- How to Motivate Students to Learn Math? [03/06/2008]
Dr. Ian replies to a question about motivating students to learn about
special quadrilaterals with some excellent general advice on
motivation, math education, and real life application of mathematics.
- If You Know Perimeter, Can You Find Area? [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?