By Martin Gardner
Aha! perception demanding situations the reader's reasoning strength and instinct whereas encouraging the advance of 'aha! reactions'.
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Extra info for Aha! Insight
It took only half an hour, and the count was 951. The computer was hooked up to a display terminal, so that it drew pictures of all the minitangrams. Read's programs are designed only for enumeration, not for solving individual tangrams. Is it possible to write a program that will inspect any given tangram and search for at least one solution? Yes, such a program has been developed and published by E. S. Deutsch, a computer scientist. In theory it is possible to write a program that will systematically examine all possible ways the tans fit a given tangram and then print all the solutions, but the complexity of such a program is so great that no one has yet attempted it.
S. Deutsch, a computer scientist with P. S. Ross and Partners in Toronto. Some of their results will be presented in the next chapter. T o whet the reader's appetite, here are two problems that will be answered in the next chapter. 1. How many different convex polygons can be formed with the seven tans? There must not be any "windows" in the figures. Rotations and reflections are not, as is customary, considered to be different. Because all three-sided polygons are convex, and no nonconvex polygon of four sides can be made with all seven tans, answering this question also gives the number of three- and four-sided polygons.
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. Equality also is transitive: ifa = b and b = c, then a = c. In everyday life such relations as "earlier than," "heavier than," "taller than," "inside of," and hundreds of others are transitive.
Aha! Insight by Martin Gardner