Archimedes' Revenge: The Joys and Perils of Mathematics by Paul Hoffman

By Paul Hoffman

An advent to the delights and demanding situations of recent arithmetic.

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Pythagoras and his followers had represented numbers as patterns of dots arranged as triangles, squares, or other geometric figures. Numbers like 3, 6, and 10 were called triangular numbers because they could be represented by dots that formed triangles: 0 * * 6 10 number of fish Simon pulled from the sea, 153, is a triangular number. By the same token, numbers 4, 9, and 16 were called square numbers because could be represented by dots arranged in squares: 0 4 @0 0 @00 0* -0000@ 3 The also like they - 00 * 000 * 0000 9 16 Archimedes' Revenge 31 Lest you think that the ancients spent long hours doodling in order to figure out whether a particular number could be represented by a particular geometric dot pattern, you should know there was a purely numerical way of finding this out.

If the Kremlin had not shown restraint, the American F-14 fighters might have encountered a squadron of Soviet MIGs instead of a defenseless civilian jetliner. When time is of the essence, codes that require elaborate machinery or sophisticated mathematical methods are impractical. In the heat of battle, for example, orders must be acted on as soon as they are received; there's not much time for deciphering. If Reagan and Weinberger had known a relatively obscure foreign tongue, they could have spoken it.

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