By Martin Gardner
Aha! perception demanding situations the reader's reasoning energy and instinct whereas encouraging the improvement of 'aha! reactions'.
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Aha! perception demanding situations the reader's reasoning strength and instinct whereas encouraging the advance of 'aha! reactions'.
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Additional info for Aha! Insight
Plenary (Holland), 1986, distributed in the United States by the University of Washington Press, Seattle. FIVE Nontransitive Paradoxes "I have just so much logic, as to be able to see . . " -ELIZABETHBARRETT, in a letter to Robert Browning. Whenever a relation R that applies to xRy and yRz also applies to xRz, the relation is said to be transitive. For example, "less than" is transitive among all real numbers. If 2 is less than 71, and the square root of 3 is less than 2, we can be certain that the square root of 3 is less than n.
It is highly unlikely that Sei Shonagon knew of the puzzle. Shigeo Takagi, a Tokyo magician, was kind enough to send me a photocopy of this rare book. Unlike the Chinese tans, the Shonagon pieces will form a square in two different ways. Can you find the second pattern? The pieces also will make a square with a central square hole in the same orientation. With the Chinese tans it is not possible to put a square hole anywhere inside a large square. Richard Reiss, a professor of English at Southeastern Massachusetts University, sent a good proof that no four-sided nonconvex polygon can be made with all 52 CHAPTER FOUR Figure 24 T h e Sei Shonagon pieces seven Chinese tans.
Dover, 1964. Diophantine Equations. Louis J . Mordell. Academic Press, 1969. A Handbook of Integer Sequences. N. J . A. Sloane. Academic Press, 1973. " Martin Gardner, in Wheels, Life,and Other Mathematical Amusements. W . H. Freeman and Company, 1983. " Harvey J. Hindin, in Journal ofRecreationa1 Mathematics 16, 1983- 1984, pp. 191- 193. " Allan Whitcombe, in Mathematics in School (a publication of England's Mathematical Association), September 1986, pp. 40 -42. The set of central figurate numbers is the "other alternative" to the vertex figurate numbers.