100 Great Problems of Elementary Mathematics
A book collecting the celebrated problems of elementary
mathematics that would commemorate their origin and, above all,
present their solutions briefly, clearly, and comprehensibly has long
seemed a necessary and attractive task to the author.
The restriction to problems of elementary mathematics was con-
sidered advisable in view of those readers who have neither the time
nor the opportunity to acquaint themselves in any detail with higher
mathematics. Nevertheless, in spite of this limitation a colorful and
compelling picture has emerged, one that gives an idea of the amazing
variety of mathematical methods and one that will-I hope-enchant
many who are interested in mathematics and who take pleasure in
characteristic mathematical thought processes. In the present work
there are to be found many pearls of mathematical art, problems the
solutions of which represent, in the achievements ofa Gauss, an Euler,
Steiner, and others, incredible triumphs of the mathematical mind.
Because the difficult economic situation at the present time barred
the publication of a larger work, a limit had to be set to the scope and
number of the problems treated. Thus, I decided on a round number
of one hundred problems. Moreover, since many of the problems
and solutions require considerable space despite the greatest con-
cision, this had to be compensated for by the inclusion of a number of
mathematical miniatures. Possibly, however, it may be just these
little problems, which are, in their way, true jewels of mathematical
miniature work, that will find the readiest readers and win new
admirers for the queen of the sciences.
As we have indicated already, a knowledge of higher analysis is not
assumed. Consequently, the Taylor expansion could not be used for
the treatment of the important infinite series. I hope nonetheless
that the derivations we have given, particularly the striking derivation
of the sine and cosine series, will please and will not be found
unattractive even by mathematically sophisticated readers.
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