Pythagorean TriplesDate: 11/19/97 at 22:41:34 From: matt Subject: Pythagorean triples I need to know the first five Pythagorean triples after 3,4,5. I think I have the first three: (20,21,29) (119,120,169) and (696, 697, 985). I also need a formula to derive Pythagorean triples. Thanks! Date: 11/20/97 at 07:30:06 From: Doctor Anthony Subject: Re: Pythagorean triples Basically you are looking for integer solutions to the equation: x^2 + y^2 = z^2 If we let x = a^2 - b^2 y = 2ab z = a^2 + b^2 Then x^2 = a^4 - 2a^2.b^2 + b^4 y^2 = 4a^2.b^2 x^2 + y^2 = a^4 + 2a^2.b^2 + b^4 = (a^2 + b^2)^2 = z^2 Thus choosing any pair (a,b) we generate a Pythagorean triplet. However, always choose these such that a > b. Example (2,1) gives x = 4 - 1 = 3 y = 2x2x1 = 4 z = 4 + 1 = 5 Example (3,2) gives x = 9 - 4 = 5 y = 2x3x2 = 12 z = 9 + 4 = 13 Example (3,1) gives x = 9 - 1 = 8 y = 2x3x1 = 6 z = 9 + 1 = 10 -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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