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

In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancée But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof Traces the origins of the Möbius strip, a sense-defying continuous loop with only one side and one edge, from the mid-1800s to the present, exploring how it has been used in mathematics, magic, science, art, engineering, literature, and music. Möbius limericks to get you in the mood -- Introduction -- Möbius magicians -- Knots, civilization, autism, and the collapse of sidedness -- A brief history of Möbius the man -- Technology, toys, molecules, and patents -- Strange adventures in topology and beyond -- Cosmos, reality, transcendence -- Games, mazes, art, music, and architecture -- Literature and movies -- A few final words -- Solutions -- References and appendix -- Readings by chapter -- About the author

the Road That Leads From The Möbius Strip — A Common-sense-defying Continuous Loop With Only One Side And One Edge, Made Famous By The Illustrations Of M.c. Escher — Goes To Some Of The Strangest Spots Imaginable. It Takes Us To Where The Purely Intellectual Enters Our World: Where Our Senses, Overloaded With Grocery Bills, The Price Of Gas, And What To Eat For Lunch, Are Expected To Absorb Really Bizarre Ideas. And No Better Guide To This Weird Universe Exists Than The Brilliant Thinker Clifford A. Pickover, The 21st Century's Answer To Buckminster Fuller.
from Molecules And Metal Sculptures To Postage Stamps, Architectural Structures, And Models Of The Universe, the Möbius Strip Gives Readers A Glimpse Of New Ways Of Thinking And Other Worlds As Pickover Reaches Across Cultures And Peers Beyond Our Ordinary Reality. Lavishly Illustrated, this Is An Infinite Fountain Of wondrous Forms That Can Be Used To Help Explain How Mathematics Has Permeated Every Field Of Scientific Endeavor, Such As The Colors Of A Sunset Or The Architecture Of Our Brains; How It Helps Us Build Supersonic Aircraft And Roller Coasters, Simulate The Flow Of Earth’s Natural Resources, Explore Subatomic Quantum Realities, And Depict Faraway Galaxies.

publishers Weekly

the Mobius 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 Mobius And Johann Benedict Listing. As Pickover (calculus And Pizza), A Prolific Science Author And Former Discover Columnist, Tells Us, Today Mobius's Strip Is Everywhere: It Forms The Familiar Recycling Symbol; Freestyle Skiers Attempt A Stunt Called A Mobius 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 A La Martin Gardner Will Get Much Pleasure From This Inviting Book. B&w Illus. (may) Copyright 2006 Reed Business Information.

The road that leads from the Mobius strip -- a common-sense-defying continuous loop with only one side and one edge, made famous by the illustrations of M.C. Escher -- goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, the price of gas, and what to eat for lunch, are expected to absorb really bizarre ideas. And no better guide to this weird universe exists than the brilliant thinker Clifford A. Pickover, the 21st century's answer to Buckminster Fuller. Come along as Pickover traces the origins of the Mobius strip from the mid-1800s, when the visionary scientist Dr. August Mobius became the first to describe the properties of one-sided surfaces, to the present, where it is an integral part of mathematics, magic, science, art, engineering, literature, and music. It has become a metaphor for change, strangeness, looping, and rejuvenation. Touching on everything from molecules and metal sculptures to postage stamps, architectural structures, and models of our entire universe, The Mobius Strip is lavishly illustrated and gives readers a glimpse into other worlds and new ways of thinking as Pickover reaches across cultures and dimensions. Clifford A. Pickover. Includes Bibliographical References (p. 217-237) And Index.