Historical Quest Here is a simple formula for finding Pythagorean triples

(numbers a, b, and c that satisfy the Pythagorean theorem). It was given to me in an elevator by my friend Bert Liberi (who is also a great mathematician). If m is any natural number greater than 1, then

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1 m m + 2 b The reduced fraction will have the property that the set (a, b, c) is a Pythagorean triple. For example, if m = 2, then 1 1 + 2 2 + 2 = 1 1 3 + - = 2 4 4 Thus, the first two numbers of the triple are 3 and 4. For the third number in the triple, we find c = 3 +4 = 9+ 16 = 25 = 5 so the set is {3, 4, 5). Find ten sets of Pythagorean triples.