Knotted Doughnuts and Other Mathematical Entertainments
Martin Gardner
Language: English
Pages: 278
ISBN: 0716717999
Format: PDF / Kindle (mobi) / ePub
Introduces puzzles and math problems involving coincidence, ciphers, games, the I Ching, geometric figures, and paradoxes.
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pauses are used as a kind of third symbol so that no more than four dots and dashes are needed for each letter. Bacon's plan was to use this cipher for concealing the plaintext (message to be enciphered) in an innocent-looking "cover text." One has only to distinguish between two different ways of printing each letter. A crude method would be to let italicized letters stand for a and roman letters for h. The word "Bacon," with only the first letter italicized, would represent the permutation
hilarious account of how he, David Ramsay and others tried to locate a treasure reportedly buried in the cloisters of Westminster Abbey. It was late at night, and a great wind developed that prevented their dowsing rods from turning. Lilly writes that he "dismissed the demons," but that the real cause of their failure was that they were surrounded by more than 30 people who kept laughing and deriding them. Lilly's autobiography is also the source of the anecdote I gave about the first meeting of
rules in reverse. There may be a better method. Indeed, there may be all kinds of clever algorithms for calculating on Napier's board, in various notations, that no one has yet discovered. ANSWERS To change a signed binary number to negabinary 1. Express the number in binary on row 2. 2. If the number is positive, move all counters that have negative values (in negabinary) down like rooks to the first row. (On a standard chessboard this means moving down all counters on white squares.) If the
If the concept is explicated within a framework of determinism, the will ceases to be free in any commonly understood sense, and it is hard to see how fatalism can be avoided. Che sara, sara. Why work hard for a better future for yourself or for others if what you do must always be what you do do? And how can you blame anyone for anything if he could not have done otherwise? On the other hand, attempts to explicate will in a framework of indeterminism seem equally futile. If an action is not
integers. In algebraic form, 1^ + 2^ + 3^ + . . . + n^ = A + 2 + 3 + . . . + nJ. An old diagram for it is shown in Figure 111. The square array of numbers. LOOK-SEE PROOFS 195 1 1 2 \ 2 4 10 33 1. 12 15 43 I 12 16 20 53 10 15 20 25 Figure JJJ 1^ + 2^ + 3^ + 4^ + 5^ = A -h 2 + 3 + 4 + 5r which extends down and right to infinity, is simply the multiplication table. Each number is the product of the number at the left of its row and the number at the top of its column. The table is divided into bent