Mathematical Entertainments
Introduction
My reasons for writing this book may very well con-
tain a clue for its understanding and enjoyment.
First, there are a great many beautiful and elegant
facts and proofs in mathematics, which are published in
widely varying places, if at all. I would like to shout
about these problems from the housetops, but have chosen
the more dignified, and probably more efficacious, method
of writing a book about them.
Second, many people consider mathematics to be a
very boring, complicated subject. I hope to show that
some facets of mathematics can be quite simple and in-
teresting, although they are not obviously so at first
glance.
Third, some of the most beautiful solutions of prob-
lems, of which I, alas, am not the originator, do not
appear anywhere to the best of my knowledge. Many I am
familiar with due only to the tenacious memory and
varied experience of M. W. Green.*
All of the problems and notes in this book have, at
one time or another, interested me very much, and I
would like to think the reader also may be fascinated by
them.
Some people may find that many problems appear to
be missing. Undoubtedly the collection is incomplete, but
all the problems I know of, and consider clever in some
tain a clue for its understanding and enjoyment.
First, there are a great many beautiful and elegant
facts and proofs in mathematics, which are published in
widely varying places, if at all. I would like to shout
about these problems from the housetops, but have chosen
the more dignified, and probably more efficacious, method
of writing a book about them.
Second, many people consider mathematics to be a
very boring, complicated subject. I hope to show that
some facets of mathematics can be quite simple and in-
teresting, although they are not obviously so at first
glance.
Third, some of the most beautiful solutions of prob-
lems, of which I, alas, am not the originator, do not
appear anywhere to the best of my knowledge. Many I am
familiar with due only to the tenacious memory and
varied experience of M. W. Green.*
All of the problems and notes in this book have, at
one time or another, interested me very much, and I
would like to think the reader also may be fascinated by
them.
Some people may find that many problems appear to
be missing. Undoubtedly the collection is incomplete, but
all the problems I know of, and consider clever in some
sense or another, are represented. Most of them can be
done mentally; none of them requires more than a single
sheet of paper. Some of the items treated here are well
known, but presented in a different way to illuminate a
different facet. I earnestly hope this book will be received
as it was intended, namely, to furnish pleasant relaxation
and to show that mathematics can be beautiful.
No preface is complete without thanks being ex-
pressed to the "person without whom this book could not
have been written." In the present case, I wish to thank
my wife.
done mentally; none of them requires more than a single
sheet of paper. Some of the items treated here are well
known, but presented in a different way to illuminate a
different facet. I earnestly hope this book will be received
as it was intended, namely, to furnish pleasant relaxation
and to show that mathematics can be beautiful.
No preface is complete without thanks being ex-
pressed to the "person without whom this book could not
have been written." In the present case, I wish to thank
my wife.
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