Pentagons and Pentagrams: An Illustrated History

by Eli Maor, Eugen Jost

Overview

A fascinating exploration of the pentagon and its role in various cultures

The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon’s wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields.

Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist’s discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon’s impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost’s superb illustrations provide sumptuous visual context, and the book’s puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.

Product Details

ISBN-13:	9780691201122
Publisher:	Princeton University Press
Publication date:	09/27/2022
Pages:	200
Sales rank:	1,071,786
Product dimensions:	8.60(w) x 5.60(h) x 0.60(d)

About the Author

Eli Maor is a former professor of the history of mathematics at Loyola University Chicago. His books include the internationally acclaimed To Infinity and Beyond, e: The Story of a Number, The Pythagorean Theorem: A 4,000-Year History, Music by the Numbers, and with Eugen Jost, Beautiful Geometry (all Princeton). Eugen Jost is a well-known Swiss artist whose work is strongly influenced by mathematics.

Table of Contents

Preface. Why the Pentagon? ix

1 Five 1

2 φ 14

Sidebar 1 Four Famous Irrational Numbers: 2 φ, e, and π 21

13 But Is It Divine? 26

4 Constructing the Regular Pentagon 38

Sidebar 2 Pentagonal Numbers 55

5 The Pentagram 58

Centerpiece. Color Plates

6 Pentastars 71

Sidebar 3 Pentagonal Puzzles and Curiosa 78

7 Tessellations: Defying the Impossible 88

8 The Discovery of Fivefold Symmetry in Crystals 103

Sidebar 4 An Unsolved Mystery 115

9 Oh, That Pentagon 119

Appendixes

A The Elementary Euclidean Constructions 133

B Three Properties of the Fibonacci Numbers 135

C A Proof That There Exist Only Five Platonic Solids 141

D Summary of Formulas 147

E Solutions to Puzzles 151

Bibliography 157

Credits 159

Index 163

What People are Saying About This

From the Publisher

“Eli Maor expertly weaves together the mathematics, history, and cultural uses of pentagons and pentagrams—shapes that have fascinated us for more than two millennia. Beautifully complemented by Eugen Jost's illustrations, this book delights and informs.”—Ian Stewart, author of What's the Use?: How Mathematics Shapes Everyday Life

"The Pentagon, famous headquarters of the US Department of Defense, is nicknamed the ‘Puzzle Palace,’ in recognition of its reputation for high adventure, deep secrets, and political intrigue. Eli Maor's book shows that the mathematical pentagon equals the military Pentagon on all three levels."—Paul Nahin, author of In Pursuit of Zeta-3

Editorial Reviews

A Choice Outstanding Academic Title of the Year

From the Publisher