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Mathematics is often presented as a large collection of disparate facts to be

absorbed (memorized!) and used only with very specific applications in

mind. Yet the development of mathematics has been a journey that has

engaged the human mind and spirit for thousands of years, offering joy,

play, and creative invention. The Pythagorean theorem, for instance,

although likely first developed for practical needs, provided great intellec-

tual interest to Babylonian scholars of 2000

B

.

C

.

E

., who hunted for

extraordinarily large multidigit numbers satisfying the famous relation a2+

b2= c2. Ancient Chinese scholars took joy in arranging numbers in square

grids to create the first “magic squares,” and Renaissance scholars in

Europe sought to find a formula for the prime numbers, even though no

practical application was in mind. Each of these ideas spurred further

questions and further developments in mathematics—the general study of

Diophantine equations, semi-magic squares and Latin squares, and public-

key cryptography, for instance—again, both with and without practical

application in mind. Most every concept presented to students today has a

historical place and conceptual context that is rich and meaningful. The

aim of Facts On File’s Encyclopedia of Mathematics is to unite disparate

ideas and provide a sense of meaning and context.

Thanks to the encyclopedic format, all readers can quickly find

straightforward answers to questions that seem to trouble students and

teachers alike:

• Why is the product of two negative numbers positive?

• What is π, and why is the value of this number the same for all circles?

• What is the value of πfor a shape different than a circle?

• Is every number a fraction?

• Why does the long-division algorithm work?

• Why is dividing by a fraction the same as multiplying by its reciprocal?

• What is the value of ii?

• What is the fourth dimension?

I

NTRODUCTION