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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New PDF release: Aha! Insight

Aha! perception demanding situations the reader's reasoning strength and instinct whereas encouraging the advance of 'aha! reactions'.

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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.