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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. Let’s 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. Let’s 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.)...
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 Spring '03
 F,newberger
 Pythagorean Theorem, Right triangle, Hypotenuse, triangle, pythagorean triples

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