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Old 2005-01-02, 03:50   #4
David John Hill Jr
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Jun 2003

22·72 Posts
Default one way to see 3 methods.

If I may refer to Heilbron's 'geometry civilized' p151,
as one of the cleanest summaries of pythagorean triplets I've run across.

Set: Generation Triplet
Pythagorean n, any odd number n,n^2-1)/2,(n^2+1)/2
Platonic n, any even number n,(n^2)/4-1.(n^2)4+1
Euclidean x,y any unequal numbers x^2-y^2,2xy,x^2+y^2

I personally found the odd case is , with some work, obvious as simply building squares on a plane. Rather enlightening an approach and exercise.
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