The Mobius Strip: Dr. August Mobius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology (Hardcover)

by Clifford A. Pickover (Author) "When I was in third grade, I went to a neighbor's birthday party that featured a magic show..." (more)
Key Phrases: cannibal torus, such caca, homed sphere, August Möbius, New York, Jos Leys (more...)

Editorial Reviews

From Publishers Weekly
The Möbius band is a puzzlingly twisted strip of paper joined at the ends with, remarkably, only one side. It was discovered separately in 1858 by German mathematicians August Ferdinand Möbius and Johann Benedict Listing. As Pickover (Calculus and Pizza), a prolific science author and former Discover columnist, tells us, today Möbius's strip is everywhere: it forms the familiar recycling symbol; freestyle skiers attempt a stunt called a "Möbius flip"; and it appears in the works of artists like M.C. Escher and writers like Arthur C. Clarke. Pickover uses the strip as a jumping-off point for a wide-ranging exploration of objects that are "chiral" (objects that are mirror images yet cannot be superimposed on each other) or have unusual properties of continuity. His travels take us from Earth, where he describes patented contraptions that incorporate the strip (a conveyor belt being one of the most successful), to the outer reaches of space, explaining some very strange topologies that have been theorized for the universe. Pickover is less successful in his forays into literature and the arts, and at times he wanders far afield. Readers who enjoy recreational mathematics à la Martin Gardner will get much pleasure from this inviting book. B&w illus. (May)
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From Booklist
Limericks, equations, quotations, patent drawings--anything pertaining to Pickover's fascination with the Mobius strip finds a place in this entertaining scrapbook of a tome. That includes biographical vignettes of nineteenth--century German mathematician August Mobius, plus cartoons of the same, which weave through Pickover's musings over the protean manifestations of the Mobius strip. The simplicity of the strip, which is formally known as a one-sided surface without identifiable direction, is a source of its ubiquity in popular awareness and parlance. Touching on plot summaries of movies and sf novels that play off the loopy continuum of the Mobius strip, Pickover underscores the high approval rating of the strip by inventors and mathematicians, for whom it is a gateway to higher dimensional space. A prolific popularizer of mathematics, Pickover is not purely an impresario here, as he delves into the strip's mathematical expression in trigonometry and complex numbers. Full of amusement and curiosity, Pickover's eclectic book should absorb the numbers set. Gilbert Taylor
Copyright © American Library Association. All rights reserved

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Product Details

• Hardcover: 304 pages
• Publisher: Basic Books; illustrated edition edition (April 27, 2006)
• Language: English
• ISBN-10: 1560258268
• ISBN-13: 978-1560258261
• Product Dimensions: 8.2 x 5.6 x 0.8 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (9 customer reviews)
• Amazon.com Sales Rank: #236,222 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

17 of 17 people found the following review helpful:

5.0 out of 5 stars A Gateway to Higher Dimensions, April 18, 2006

By	Paul Moskowitz (Yorktown, NY) - See all my reviews (REAL NAME)

The Mobius strip, the object, is itself seemingly simple. To make one is easy: take a strip of paper, give one end a half twist, and join the two ends together. The result is a loop with remarkable properties. It has only one edge and only one side. There is also a three-dimensional analog of the Mobius strip, the Klein bottle. It has only one surface. Any liquid placed in a Klein bottle coffee mug is both inside and outside the mug at the same time, as is everything in the Universe.

The Mobius Strip, the book, explores the properties of the Mobius strip as well as other topological topics, knots, higher dimensional objects, and stories and films in which space-time is looped. Pickover details the life of August Mobius and his scientific accomplishments. Interestingly, Mobius's work on the strip named for him was not published until after his death. Far from being just a mathematical curiosity, the Mobius strip is the basis for many inventions. Each chapter in the book starts with a diagram taken from a United States patent that uses the strip in some manner.

Pickover injects his own imaginative take on the meaning of the strip. For example, he supposes a town in which the bicycle path takes you around a Mobius route in such a way that you return to the start with your left and right sides reversed. It takes two trips around the path for you to get back to the way you were when you started, Interestingly, the spin-1/2 sub-nuclear particles share this characteristic. Perhaps electrons and protons are very small Mobius strips.

In this volume, the author builds upon his previous mathematical works, Wonders of Numbers, and A Passion for Mathematics. There are puzzles for each chapter. This book focuses on topological subjects, but also includes the human side of the story. It is infused throughout with Pickover's unique view of reality. While, there are a few esoteric equations, these can be skipped without loss by those who are so inclined. This is perhaps Pickover's best and most interesting work combining fascinating mathematics with the history of its creation. More biographical sketches can be found on his "Six Thousand" web site where he profiles creative artists, writers, scientists, and other thinkers.

10 of 10 people found the following review helpful:

5.0 out of 5 stars A Magical Trip with "The Mobius Strip", June 11, 2006

By	Ray Erskins (La Porte, TX) - See all my reviews (REAL NAME)

Permit me to rave about "The Mobius Strip." Then buy it, read it, and enjoy its many flavors. Math buffs will find it as mouth-watering as a bowl of Ben and Jerry's ice cream. The aesthetically inclined will be delighted by its initial simplicity and the helpful illustrations that enable them (and me) to grasp the book's mathematical profundities.

Always the entertainer, Cliff Pickover takes the stage with "Mobius Limericks to Get You in the Mood." Soon after we see a photo (by Paul Mobius) of his father's skull with Beethoven's skull grinning in the foreground. Shades of P.T. Barnum! And this is only the introduction!

Although the ideas in the book are presented with exceptional clarity and treated with utmost respect by the author, he does reveal his dry sense of humor upon occasion. Here is one of my favorite nuggets on page 11:

"One of the most mystifying Mobius arrangements is the sandwich Mobius strip, created with just two strips of paper. I have known people to ponder this for hours while listening to Pink Floyd without ever fully appreciating what they have beheld."

This gives you some idea of what's in store for the perceptive reader. The book swiftly advances beyond parlor tricks, toys, patented inventions, sailor's knots, the Book of Kells, and other amazing items until we find ourselves soaring into the realm of transcendental reality. One gets the feeling that the Mobius strip is the skeleton key to infinity. But then, so is the Klein bottle. So is Alexander's horned sphere. So is the Penrose triangle. So is M.C. Escher's art! The book is filled with these enigmatic jewels of understanding.

As the complexity of the kaleidoscope intensifies, Cliff Pickover suddenly becomes a fractal Will Rogers, dazzling us with topographical rope tricks. Strange loops are explained as he twirls them before our very eyes! Your mind is turned into a pretzel as your train of thought is twisted into a trefoil knot made of interlocking, multi-colored puzzle pieces. Notice the cover!

You may have to listen to the Moody Blues, Tangerine Dream, Enya, and Pink Floyd to fully grok the cosmological essence of all he has to say in this sweet little book. But it is well worth the effort. In the final chapters he connects all this to games, mazes, art, music, architecture, even literature and movies. Your powers of observation will only increase as you plunge deeper into Pickover's topographical ocean.

8 of 8 people found the following review helpful:

5.0 out of 5 stars John - A Twisted Space Enthusiast, June 29, 2006

By	J. K. Carrington Exp "Rubber Geometry Enthusiast" (Toronto, Canada) - See all my reviews (REAL NAME)

WoW! Another great book by Clifford Pickover. Math buffs and recreationists alike will love this book. This is a readable, non-technical tour de force of the Mobius band and its ubiquitous presence. Don't be fooled by my "non-technical". The concepts covered here will stretch the mind of most anyone not already thoroughly immersed in rubber geometry. The strip wends its one-sided way through knots, magic tricks, toys and games, hyperspace, art, architecture and even literature.

My only plea would be to have some of the illustrations in colour.

Highly recommended!