The Book of Numbers by John H. Conway and
Richard K. Guy, Copernicus, $29, ISBN 0 387 97993 X
In Britain in September, Springer, 拢19.50
WHILE on his travels, the Polish mathematician Waclaw Sierpinski became
convinced that he鈥檇 lost a piece of luggage. 鈥淣o, dear,鈥� said his wife, 鈥渁ll six
pieces are here.鈥� 鈥淭hat can鈥檛 be true,鈥� protested the mathematician. 鈥淚鈥檝e
counted them several times: zero, one, two, three, four, five.鈥� There is a
serious point to this apocryphal tale: it relates to a classic way of defining
numbers according to set theory. You can find out all about that in The Book
of Numbers.
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This is a book to dip into: its many short sections are filled with cute
nuggets of information. I was a bit disappointed to find that much of the
material is 鈥渙ld standards鈥�. But much of modern mathematics is esoteric, and the
great feature of Numbers is that anyone can read it without excessive
head scratching. And John Conway and Richard Guy do mix surprises in with the
golden oldies.
A rich haul, Numbers includes Ramanujan鈥檚 formula for partitions,
the factors of the 13th Fermat number, 17-sided polygons, Farey sequences,
Pythagorean fractions, the game of Hackenbush and surreal numbers.
This is the great charm of mathematics: its ability to turn up apparently
grotesque freaks, then reveal them as lustrous creatures of beauty and
significance. You鈥檒l find plenty here to keep you occupied, amused and informed.
Buy, dip in, wallow.