Mathematics on Vacation - ISBN:0684139642

Mathematics on Vacation

Date: 28 April 2011, 03:08

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Mathematics on Vacation
By J. S. Madachy
* Publisher: Scribner
* Number Of Pages: 252
* Publication Date: 1975-05 (pbk of 1966 edition)
* ISBN-10 / ASIN: 0684139642
* ISBN-13 / EAN: 9780684139647
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.
1
• GEOMETRIC DISSECTIONS
2
• CHESSBOARD PLACEMENT PROBLEMS
3
• FUN WITH PAPER
geometric constructions with paper only
flexagons
other flexagon diversions
solid flexagons
4
• MAGIC AND ANTIMAGIC SQUARES
magIc squares
miscellaneous magic configurations
antimagic squares
talisman squares
contents
5
• PUZZLES AND PROBLEMS
problems
answers
6
• NUMBER RECREATIONS
numbers and their divisors
perfect and multiperfect numbers
prime numbers
amicable numbers
0123456789, or digital diversions
narcissistic numbers
factorial products
printer's "errors"
automorphic numbers
two rather large numbers
7
• ALPHAMETICS
alphametic puzzles
answers
8
• CONGLOMERATE
the problem of the mice
deployment
domino recreations
lost chords
bouncing billiard balls
• GLOSSARY
• BIBLIOGRAPHY
• INDEX

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