The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Coordinate/Analytic Geometry and the Pythagorean Theorem

Date: 6/11/96 at 9:36:49
From: Anonymous
Subject: Pythagoras' theorem

I am a mechanical engineer from Sweden. I have a simple question on 
coordinate geometry (or analytic geometry).

How can you prove Pythagoras' theorem with pure coordinate methods?
Usually the concept "distance" is introduced in coordinate geometry by
using Pythagoras' theorem, but I want to prove it with the methods of
coordinate geometry.

Thank you
John Engel

Date: 9/5/96 at 12:19:20
From: Doctor Ceeks
Subject: Re: Pythagoras' theorem


The Pythagorean theorem was most likely originally intended as a 
statement about the areas of squares erected on the sides of a right 

If you view the theorem in this manner, then to prove it using 
coordinate geometry you would have to define notions of area and also 
of angle, so that you can speak of "right" triangles.  Doing so would 
probably amount to a translation of the existing proofs.

The notion of distance is tricky, and you're right that Euclidean 
distance is very often built into the definition of coordinate 

However, it is well known now that Euclidean distance isn't the only 
meaningful distance to define on the coordinate plane (= pairs of 
reals (x,y)).

So the answer to your question depends on what you mean by "pure 
coordinate methods".

-Doctor Ceeks,  The Math Forum
 Check out our web site!   
Associated Topics:
College Coordinate Plane Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.