Paul C. Pasles - Benjamin Franklin’s Numbers

Benjamin Franklins Numbers

Benjamin Franklins Numbers

An Unsung
Mathematical Odyssey

Paul C. Pasles

PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD

Copyright 2008 by Princeton University Press

Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540

In the United Kingdom: Princeton University Press, 3 Market Place, Woodstock, Oxfordshire OX20 1SY

All Rights Reserved

British Library Cataloging-in-Publication Data is available

Library of Congress Cataloging-in-Publication Data

Pasles, Paul C., 1968
Benjamin Franklins numbers : an unsung mathematical odyssey / Paul C. Pasles.

p. cm.

Includes index.

ISBN-13: 978-0-691-12956-3 (hardcover : alk. paper)

eISBN-13: 978-0-691-22370-4 (ebook)

ISBN-10: 0-691-12956-8 (hardcover : alk. paper)

1. Franklin, Benjamin, 17061790. 2. MathematicsHistory. 3. Magic squares. 4. Mathematical recreation. I. Title.

QA24.P37 2008

510.92dc22

2006102508

For Antoinette
who loved history

and Anthony
who loves to count

Preface

Few lives have been as well examined as that of Benjamin Franklin. New biographies continue to spring forth regularly, with no end in sight. Somehow, though, the mathematical side of that great mind remains unstudied. Hence the present book, Benjamin Franklins Numbers.

Scattered throughout this historical account are various mathematical questions. You may decide to attempt some, all, or none of these exercises, depending on your personal preferences (and your mathematical background); but at least read them, to see what mathematics can do. Their actual solution is not necessary for a proper reading of this book.

Seventeenth-century documents present some peculiar challenges. Often I have updated or corrected spellings, capitalization, and punctuation. In other cases, when it is not too distracting, the original text has been left unmolested, the better to convey some sense of authenticity. I make no claim of consistency on this score.

I have not written anything resembling a complete biography. As with all great lives, Franklins life appears to us as a magnificent jigsaw puzzle with a few pieces missing. With this book, I hope to fit one more piece firmly in its place.

Benjamin Franklins Numbers

1The Book Franklin Never Wrote

It seems to me, that if statesmen had a little more
arithmetic, or were more accustomed to calculation,
wars would be much less frequent.

Benjamin Franklin (1787)

The American author Ernest Hemingway never composed a guide for writers. Indeed, the very idea was anathema to him, in part because of a superstitious fear that any such discussion of his art would destroy the thing itself, just as dissecting a flower dissolves the very essence of its beauty.