Download Game, Set and Math: Enigmas and Conundrums by Ian Stewart PDF

By Ian Stewart

A set of Ian Stewart's leisure columns from Pour los angeles technology, which display his skill to convey sleek maths to lifestyles.

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Additional info for Game, Set and Math: Enigmas and Conundrums

Sample text

Perle explained it this way: As you pronounce the word you sweep out all possible triples of short and long beats. The first three syllables, ya md td, have the rhythm short, long, long. The second through the fourth are md td rd: long, long, long. " There are eight d istinct triple s of rhythms, long or short; you can check that each occurs in the nonsense word exactly once . Stein reduced the word to its mathematical content by using0 for short and 1 for long, so that it became 0111010001. After staring at the simplified string for a while, I noticed a lovely thing.

1 Electron-hole pairs are electrically neutral. If electrons (black) are moved through an infinite system ofholes, it is possible to create a free electron from nothing, in violation of the Law of Conservation of Energy. The beginning of the GALILW file, containing an infinite amount of information. What does the file list and how is the information coded? 1 ! 1 ! 0! 1 ! 1 ! o! 1 11 ! 1 1 1 1 ojojo! ojojo l 1 ! 3 Toadd a digit 1 at thefront ofthefull GALILW file,just move each digit up one place.

The mind boggles. Yamtittirtijabhdnasalagtim . . ANSWERS Four-digit pairs: using Martin's algorithm, you get 001 1223321310302 Three-digit quadruples: the same method yields 00001 1 1 12222122112121 1 1 02220221021202110122012101 1201 10022 00210012001020201010002 A 4 x 4 ourotorus (it is essentially unique) is shown in figure 4 . 8 . If its design is repeated as shown, you get a remarkable tiling of the plane by cross-shaped dark and light tiles, in which all possible 2 x 2 arrays of dark and light squares appear in a regular manner.