Customer Reviews

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

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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.

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!

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.

I first heard of Cliff Pickover while exploring fractals and strange attractors as art, and eventually I found myself hearing more and more about this prolific author.

Eventually I had the opportunity to read this book.

A scrapbook of a great mind, allowing us to follow the Moebius strip through history as a mathematical entity and as a metaphor for everything from the process of learning to the very nature of our universe. It's a fascinating and accessable read for the incredibly thought provoking nature of the information therein; sharing in Pickovers' enthusiasm and imagination makes it even more so. I thoroughly enjoyed it, and look forward to reading it again, as well as tracking down more of Pickovers' work.

If I could compare it to anything in current literature, it'd be Simon Winchesters' Krakatoa.

The mobius strip - a continuous loop with only one side and one edge - was popularized by the illustrations of M.C. Escher, yet few know of its history and the evolution of its concept. Drive Clifford Pickover here provides a lively survey of the strip from the mid-1800s when Drive Mobius described it, to its influence in the fields of math, science, engineering, and the arts. It's more than a concept: it offers up new methods of thinking and discussions here include related shapes and ideas as well.

Diane C. Donovan
California Bookwatch

In 1633, Galileo Galilei said, "The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language... without which it is humanly impossible to comprehend a single word." And so begins Dr. Pickover's amazing roller-coaster ride through a breathtaking array of topics in science and art.

Some of the book deals with topology and "glistening shapes that span dimensions." Other portions concern the Mbius strip in countless settings, from molecules and metal sculptures to postage stamps, literature, architectural structures and models of our entire universe. The strip is featured in countless technology patents, which decorate the frontispieces of each chapter.

In some of the most impressive chapters, Pickover deals with endless loops in literature and mythology. He also coaxes readers to question the way they see the world and think about reality. For example, readers will become more conscious about what it means to visualize a one-sided object or what it means to have orientation-reversing paths in space.

Pickover also has a penchant for knots, and he notes that knots have been crucial to the development of civilization, where they have been used to tie clothing, to secure weapons to the body, to create shelters, and to permit the sailing of ships and world exploration. He also suggests that knot patterns have been found on burial stones engraved by Neolithic peoples. Today, knot theory has infiltrated biology, chemistry and physics. Pickover writes, "In a few millennia, humans have transformed knots from ornamental engravings on rocks to models of the very fabric of reality." I enjoyed this book immensely and recommend it to all readers interested in the science of imagination.

If the book of nature is written in mathematics, then the works of Clifford Pickover can safely be said to be a great Cliff's Notes version!

In all his work, Pickover has a genuine gift for making the abstract accessible and meaningful like here where he discusses perhaps the most famous creation of August Mobius: the Mobius strip.

To make one is very easy: 1) cut out a piece of paper in the shape of a ruler, 2) take one edge of the paper, turn it 180 degrees and 3) join it with the other end of the paper.

As a result of this operation, you will have created a circular looking object with a kink in the middle. That kink does something fascinating: it makes it so that if you trace your finger along the surface of the object, you will find that it only has one side!

As paradigm defying as this may seem, it litterally opens the door to interesting discussions about the various topologies (or surface formations) an object can assume. It begins a discussion of different dimensions and the exotic mathematics that describe them.

Filled with easy to follow discussion and lots of pictures, Pickover takes great pains to make sure he never leaves any readers behind.

This book is great and those who really enjoyed would be well advised to also read Pickover's Surfing Through Hyperspace and also his Time: A traveler's guide.

In this book, Clifford Pickover once again verifies a statement that I used many years ago to describe him, "A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today." The Mobius strip is an extremely simple device, yet the analysis of it leads to an enormous variety of complexity. It is nothing more that a continuous strip of paper with a half-twist in it. There is only one side and it is used for everything from an amusement to a model for the fundamental shape and structure of the universe.
Pickover covers this wide spectrum as well as some historical background on the inventor; German mathematician Dr. August Mobius, a student of Gauss who lived in the middle 1800's. This was a nice inclusion, as the history of the principal creators of mathematics is often overlooked. An historical oddity that Pickover also brings up is that it is somewhat surprising that this simple device was not invented until the 1800's. Given the incredible simplicity, it is indeed odd that no one had ever considered it until then.
Once again at his best, Pickover follows a trail that only he seems capable of blazing. His writings are entertaining, profound and illuminate an area of mathematics in a manner that non-mathematicians can follow, appreciate and understand.

Clifford Pickover's "The Mobius Strip" is a great book with easy to understand explanations of the one sided Mobius Strip and other fascinating mathematical and scientific matters. Once I began reading it, I could not put it down. I know next to nothing of math or science, but this book helped me understand concepts and facts most people don't know. It was a very enjoyable read, and I learned a lot from it. I say everyone should read this book. It will open your eyes to awesome possibilities and fascinating facts and trivia. There's nothing really I can say about this book except it's a tremendously fun, informative, intelligent, excellent read. A++++!

Not a math geek, didn't know anything about this area but wanted to learn something new. I have, interesting book.