Copyright ©2008 by Paul Niquette. All rights reserved..
asks for the formula that generates a family of right
the indicated Natural Hypoteneese
with 3|4|5, 5|12|13, 7|24|25, 9|40|41. Two
You might enjoy proving that these formulas work for all values of n...
[2n +1]2 + [2n(n + 1)]2 = [2n(n + 1) +1]2
You might also enjoy exploring the question of how many Natural Hypoteneese there are. Well, of course, there is an infinite number -- in each family. Still, there are plenty of integers that are not Natural Hypoteneese. The graph below shows the cumulative Natural Hypoteneese in relation to the natural numbers.
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