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 Hi, The Pythagorean theorem was most likely originally intended as a statement about the areas of squares erected on the sides of a right triangle. 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 geometry. 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! http://mathforum.org/dr.math/
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