See also the
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.
- Deriving Pi [05/10/2001]
I know that Pi is equivalent to 3.14, but what formulas are used to come
up with 3.14?
- Deriving the Midpoint Formula [08/08/1999]
How is the midpoint formula derived from the distance formula?
- Desargues' Theorem [09/22/1999]
What is Desargues' theorem and how can it be proven?
- Desargues' Theorem and SSASS [12/15/1998]
What is the main theory behind Desargues' Theorem? Also, is SSASS a valid
method for proving two quadrilaterals are congruent?
- Descartes' Square Root Method [10/30/1996]
Why does Rene Decartes' geometric method for finding square roots work?
- Determine if Point is in Rectangle [5/29/1996]
What formula will allow me to determine whether a specified point lies
within a polygon (rectangle - 4 points)?
- Determining Equable Shapes [06/15/1999]
Could you please list some equable shapes and show me how you determined
- Determining Length of Material Remaining on a Roll [11/24/2003]
Is there a mathematical formula to determine the length of material on
a roll, given the outside diameter of the core, the outside diameter
of the whole roll, and the thickness of the material (determined by a
- Determining the Length of a Coil of Ribbon [08/31/2001]
How will calculus give me the same answer I found with algebra and
- Diagonals and Tiles [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?
- Diagram to Prove Difference of Squares Formula [06/18/2008]
I was able to make a picture showing why (a+b)^2 = a^2 + 2ab + b^2 by
having a square with sides a+b and getting four areas within the
square. But I can't figure out how to show that a^2 - b^2 =
(a+b)(a-b) using a similar diagram.
- Diameter Endpoint [01/26/2003]
The center of a circle is (-4,7) and one endpoint of a diameter is
(2,-1). What is the other endpoint of the diameter?
- Dimensions [08/30/2001]
What are 1-dimensional, 2-dimensional, and 3-dimensional? What's the
- Distance between Points of Tangency [02/16/2003]
Two circles, one of radius 5, the other of radius 8, intersect at
exactly one point, and the center of each circle lies outside the
other circle. A line is externally tangent to both circles. Find the
distance between the two points of tangency.
- Distance From a Point to a Line [09/16/1998]
Derive an equation to give the distance from any point on a 2D plane to a
- Distance from a Point to a Line [08/20/1999]
Can you show me a straightforward way to derive the formula for the
distance from a point to a line: abs(Ax+By+C)/sqrt(A^2+B^2)=D?
- Distance from Point to Ellipse [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?
- Dividing a Circle into 8 Equal Parts [08/19/2002]
If you have a diameter of 14 ft., can you mark off the 1/8 sides of
the circumference so that they are equal?
- Dividing a Line Segment [03/08/2001]
How do I divide a line segment into a 2:3 ratio using the angle bisector?
- Dividing Land by Area vs. Perimeter [11/05/1999]
What are the advantages of dividing land by area vs. perimeter?
- Does Trying to Square a Circle Cause an Illness? [03/14/2006]
I've heard that people thought that trying to square a circle was an
illness. What was that illness called?
- Drawing a Locus of Points [05/30/2008]
Draw the locus of all points in the plane that are equidistant from
the rays of an angle and equidistant from two points on one side of
the angle. I'm having trouble with this kind of locus problem. Can you
explain how to think about and solve them?
- Eleven Nets of a Cube [11/15/2001]
My teacher says that there are 11 combinations to make a cube without
reversing them, but I can only find 6.
- Enlarging the Penguin Pond [06/03/1999]
By how much should its length and width be increased to double the area
of the 12 meter x 8 meter penguin pond at the zoo?
- Equable Polygons and the Area of a Circle [10/30/2001]
I have found a general formula to work out the side length a polygon (of
any shape) must have to be equable, which is closely linked to finding an
equation for the area of a circle without using pi (and therefore proving
- Equable Polygons [10/29/2001]
I need a formula for finding equable polygons. I know the formula 4/
tan(90-180/n), but how do you get to this point?
- Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]
What are the origins and roots of the words geometry, algebra, and
- Euclid's Fifth Postulate [6/24/1996]
I am interested in finding some theorems, axioms, or postulates similar
to Euclid's Fifth Postulate.
- Euclid's Parallel Postulate [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?
- Euler's Formula [11/26/2001]
I have to find Euler's formula for two-dimensional figures and explain it
at a university level and at an elementary-school level.
- Fabric Left on a Roll [03/15/2001]
I am going to write a program for my TI-83+ to calculate how many feet of
material are left on a roll.
- Figure Not Drawn to Scale [08/16/2003]
A line l is drawn with points A,B,C,D,E, and F, in that order. The
points appear equidistant, the figure is not drawn to scale. If AD=BE,
which of the following must be true?
- The Figure of Maximum Area and Given Perimeter [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? What are the dimensions of a triangle with perimeter p that encloses the maximum area?
- Figuring Out Formulas for Area [08/24/1999]
How can I remember formulas for squares, triangles, cylinders, etc?
- Filling a Garden with Topsoil [2/5/1996]
I have a garden that is 10' x 10' (100 square feet). I want to add 6" of
topsoil to my garden. Topsoil is sold by the cubic yard. How many cubic
yards of topsoil will I need for my project?
- Find Angle DEA and Angle ADB [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.
- Finding a Locus of Points from a Description [03/30/2004]
I am trying to help my son figure out these three questions, but we
aren't sure what is meant by "locus". Is there a formula to use?
- Finding an Angle Between Tangent Lines [10/19/2003]
How do I find the angle between the tangents to the graphs of y = e^(x)
and y = e^(-x) at the point of intersection?
- Finding Areas of Different Polygons [09/02/1997]
Could you please tell me how to work out the area for an equilateral
heptagon, octagon, nonagon, decagon, unedecagon, and dodecagon?
- Finding Captain Kidd's Treasure [05/17/2000]
How can you find Captain Kidd's treasure if you can't find the tree
referenced in the instructions?