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J. S. Madachy, ""

preface

If you have ever solved a mathematical puzzle, played any game in

which numbers were used, learned a number trick, or played ticktacktoe,

you have indulged in a type of mathematical recreation. In general,

these recreations share three characteristics: first, they are mathematical

or logical; second, they are fun; third, they all appear to be quite useless.

The first two characteristics require no support, but some might ask

why anyone should indulge in anything that is of no practical value. An

indirect defense may be built up from the fact that the most staid mathematics

and engineering journals publish some material that is strictly

recreational in nature, giving the amusements a kind of endorsement.

Moreover, a very cursory examination will disclose a few interesting

facts about the utility of recreational mathematics. Prime numbers, for

example, have no practical value. It may be decades, if ever, before such

a use for them will be found. However, the study of prime numbers and

their properties has filled many a gap in the field of number theory, that

mathematical discipline which studies the basic properties of all numbers.

Magic squares have been involved with superstitious beliefs and

proven an interesting source of amusement for centuries. They, too, offer

practical rewards for the agricultural and nuclear scientist. The study of

the patterns of certain types of magic square has shown how to reduce

the number of experiments required to obtained growth and radiation

data. The classic Moebius strip has been used for conveyor belts that

last twice as long as conventional belts. Indeed, the B. F. Goodrich Co.

has obtained a patent for this particular use. Many areas of recreational

mathematics still seem to be useless, but who can say what next year

or the next decade will bring?

This book attempts to give a sampling of both types of material. Much

of its material is taken from the pages of Recreational Mathematics Magazine,

which I founded, edited, and published from 1960 until its discontinuation

in 1964. Moreover, many notes and comments from the

periodical's readers as well as a number of original ideas have been

incorporated here.

Thanks and direct acknowledgement to the many who contributed or

helped will be found in the Acknowledgements and throughout the book.

Thanks must also go to]. A. H. Hunter, Howard C. Saar, and Dmitri

E. Thoro who, as co-editors of Recreational Mathematics Magazine, worked

far beyond the call of duty. The author wishes to express his gratitude

as well to the nearly ten thousand former subscribers whose enthusiasm and

support helped make this book possible.

Kettering, Ohio J.S.M.

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