Mathematical Recreations and Essays

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This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" ? The Mathematics Teacher. Index. References for Further Study. Includes 150 black-and-white line illustrations.
 

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Зміст

ARITHMETICAL RECREATIONS
3
Four fours problem
16
Nim and similar games
36
Bachets weights problem
50
Rational rightangled triangles
57
Mersenne numbers
64
Galois fields
73
Geometrical paradoxes
84
Magic squares of a singlyeven order
196
Magic squares of nonconsecutive numbers
210
Unbounded surfaces
232
Number of ways of describing a unicursal figure
250
Dragon designs
266
COMBINATORIAL DESIGNS
271
Kirkmans schoolgirl problem
287
Lines in higherdimensional space
303

Cyclotomy
94
Addendum on a solution
102
Dynamical games of position
116
Paradromic rings
127
POLYHEDRA
130
The Archimedean solids
136
The KeplerPoinsot polyhedra
144
Regular sponges
152
CHESSBOARD RECREATIONS
162
The eight queens problem
172
MAGIC SQUARES
193
The Tower of Hanoi
316
The window reader
333
The trisection of an angle
344
CALCULATING PRODIGIES
360
Bidder 18061878
367
Safford 18361901
374
Alexander Craig Aitken
386
Transposition systems
391
Substitution systems
402
Determination of cryptographic system
414
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Про автора (1987)

H. S. M. Coxeter: Through the Looking Glass
Harold Scott MacDonald Coxeter (1907?2003) is one of the greatest geometers of the last century, or of any century, for that matter. Coxeter was associated with the University of Toronto for sixty years, the author of twelve books regarded as classics in their field, a student of Hermann Weyl in the 1930s, and a colleague of the intriguing Dutch artist and printmaker Maurits Escher in the 1950s.

In the Author's Own Words:
"I'm a Platonist ? a follower of Plato ? who believes that one didn't invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."

"In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles, and spheres are seen to behave in strange but precisely determined ways."

"Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry."

"Let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused." ? H. S. M. Coxeter

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