This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: For example, 3, 4, 5 6, 8, 10 (times 2) 9, 12, 15 (times 3) 1.5, 2, 2.5 (times 0.5) These are all Pythagorean Triples. Lets see what happens if we have a triangle that is not a right triangle. I know that equilateral triangles are not right. So if I take a triangle with sides all 1 and I try to use the Pythagorean Theorem, I get 1^2 + 1^2 = 1^2 or 2 = 1, which is nonsense. So I have shown that if a triangle does not have a right angle, then we do not always get a ^2 + b ^2 = c ^2. If I know any two sides of a right triangle, then I can always find the third. Lets see what happens if we fix a = 1 b x 0 1 2 3 4 5 6 7 8 c ( x ^2 + 1) 1 2 3 2 5 6 7 8 3 So if a = 1, then we can think of c as a function of b , namely c is f ( x ) = ( x ^2 + 1). b or x c or f ( x ) (Note that this is about 350 words.)...
View
Full
Document
This note was uploaded on 01/12/2010 for the course MATH 247 taught by Professor F,newberger during the Spring '03 term at Stanford.
 Spring '03
 F,newberger
 Pythagorean Theorem

Click to edit the document details