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Science Frontiers ONLINE No. 74: Mar-Apr 1991 |
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Pi Surprise
Consider the positive integer, 8. It can be written as m 2 + n 2 , a sum of two squares of integers, in just 4 ways, namely when the pair (m, n) is (2, 2), (2, -2), -2, 2), and (-2, -2). The integer 7, on the other hand, cannot be written as the sum of any squared integers. On the average, over a very large collection of integers from 1 to n, in how many ways can an integer be written as the sum of such squares? The answer is little short of astounding: closer and closer to pi!
(Anonymous; "Closing Pi Surprise," Algorithm, p. 7, n.d. Cr. C.H. Stiles)