Mathematics is often absorbed (memorized!) and presented as a large collection of disparate facts used only with a very specific application in mind. However, the development of mathematics has been a journey that has engaged the human mind and spirit for thousands of years, providing pleasure, play, and creative invention.
For example, the Pythagorean Theorem was probably first developed out of practical necessity, but it also provided great intellectual interest to Babylonian scholars in 2000BC in their search for very large multi-digit numbers that satisfied the famous relationship a 2 + b2 = c2. Ancient Chinese scholars delighted in arranging numbers on a square grid to create the first “magic square,” and European Renaissance scholars tried to find a formula for prime numbers, although they had no practical application in mind.
These were the Diophantine equation, the half-magic square, the Latin square, and public key cryptography in general. Most concepts presented to students today have a rich and meaningful historical place and conceptual background. The purpose of Facts on File’s Encyclopedia of Mathematics is to integrate disparate ideas and provide a sense of meaning and context.
About the Book
This one-volume encyclopedia for high school and early college students, with over 1,000 entries and more than 125 photographs and illustrations, brings disparate ideas together and explains the meaning, history, background, and relevance of each.
The text also goes further and presents proofs for many of the results discussed. For example, one can find under the relevant sections the proof of the Fundamental Theorem of Algebra, the proof of Descartes’ law of signs, the proof that every number has a unique prime factorization, the proof of Brettschneider’s formula (a generalization of Brahmagupta’s famous formula), the derivation of Heron’s formula, and more. Such content is rarely found in standard math textbooks.
Where the method of proof is beyond the scope of the text, at least a discussion of the method behind the proof is provided. (For example, an argument is given showing how a formula similar to Stirling’s formula can be obtained, and a discussion of the Cayley-Hamilton theorem shows that every matrix satisfies at least some polynomial equation.) This encyclopedia is intended to satisfy people at all levels. Each entry has cross-references to other entries, providing further context and opportunities to explore related ideas. Readers are encouraged to browse.