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This book is one of a series written by professional mathematicians in
order to make some important mathematical ideas interesting and under-
standable to a large audience of high school students and laymen. Most of
the volumes in the New Mathematical L i h y cover topics not usually
included in the high school curriculum they vary in difficulty, and, even
within a single book, some parts require a greater degree of concentration
than others. Thus, while the reader needs little technical knowledge to
understand most of these books, he will have to make an intellectual
effort.
If the reader has so far encountered mathematics only in classroom
work, he should keep in mind that a book on mathematics cannot be read
quickly. Nor must he expect to understand all parts of the book on first
reading. He should feel free to skip complicated parts and return to them
later often an argument will be clarified by a subsequent remark. On the
other hand, sections containing thoroughly familiar material may be read
very quickly.
The best way to learn mathematics is to do mathematics, and each
book includes problems, some of which may require considerable
thought. The reader is urged to acquire the habit of reading with paper
and pencil in hand in this way mathematics will become increasingly
meaningful to him