Pentagons and Pentagrams: An Illustrated History

by Eli Maor, Eugen Jost

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.

Genres: Mathematics

200 pages, Hardcover

Published September 27, 2022

Reviews

[Wing · Rating 5 out of 5]

This is a very light mathematics book. Indeed, at least half of it is devoted to non-mathematical subjects such as art, architecture, and chemistry. As usual, Maor keeps the reader engaged by explaining things slowly and carefully. He also relegates the more demanding material to the appendices so as to preserve the flow of the text. As he repeatedly points out, it is remarkable that arithmetic can be so miraculously linked to geometry, particularly in the context of the so-called golden ratio and the Fibonacci sequence. The infinitely nested radical and continued-fraction expressions of the former are truly “divine”. Only a rudimentary knowledge of mathematics is required; indeed, there is no calculus or trigonometry involved. Very satisfying. Five stars.

[teehee · Rating 5 out of 5]

The peak of a book meant to encourage interest in maths for general public. Imagine a tireless list of architectural examples of pentagons, three slightly more intensive maths topic, sprinkle the former in between the latters is basically the structure of the book.

It is well-proportioned and tells me just enough to explore on my own without feeling too bored if I know nothing about geometry (most material is from grade 7 geometry/ algebra)

[George · Rating 3 out of 5]

Interesting if you like math, mythology, and history. I have it 3 stars because it vacillates between very readable/accessible and dense mathematical formulas.
If you studied math in college, you shouldn’t have any trouble with this, but otherwise some of the book is too dense.

[Iamreddave · Rating 4 out of 5]

Interesting historical book about pentagons through history. Crystals, Romans, Forts, Floors all get a look in. The images are great and the Maths pretty accessible .