Introduction
In which we encounter a "hole through a hole in a hole," topology, Mobius
strips, the desiccated skull of Mobius, Franz Gall, the recycling symbol, Mobius
beer, the "Mobius Flip," Max Bill's "Endless Ribbon," Gustavo Mosquera, Eternal
Sunshine of the Spotless Mind, M6bius strip metaphors, Mobius strips in reli-
gion, Eugene lonesco's play The Bald Soprano, the cerebral Mobius strip, and
the Acme Klein bottle.... xv
Mioblus Magicians
In which we encounter Mobius illusions, gospel magic, the Mobius treadmill
puzzle, Mobius's place in history, and my boyhood introduction to the mar-
velous band.... 1
2.
Knots, Civilization, Autism, and the Collapse
of Sidedness
In which we encounter ants inside spheres, Mobius dissections, sandwich
Mobius strips, Ljubljana ribbons, Lord Kelvin's vortex knots, trefoil knots, New
York lawyer and part-time topologist Kenneth Perko, the mystery unknot,
Asperger's syndrome, Wolfgang Haken's unimplementable knot algorithm, the
triquetra, the occult TV show Charmed, Led Zeppelin, The Book ofKells, knots in
proteins, Borromean rings, knots as catalysts of civilization, the alien knot
puzzle, and Mobius aliens.... ?
A Brief History of Mobius the Man
In which we encounter Mobius's family tree, simultaneity in science,
Schulpforta, Paul Julius Mobius, Mobius syndrome, Johann Benedict
Listing, the "king with five sons" problem, Mbbius's mathematical output,
Karl August Mobius, the false dawn animal, the M6bius maze puzzle, and
M6bius licentiousness.... 25
Technology, Toys, Molecules, and Patents
In which we encounter the Rhennius machine, Roger Zelazny's Doorways in
the Sand, Mobius patents and toys, Mobius molecules, mathematics patents,
lemniscates, astroids, Reuleaux triangle drill bits, conveyor belts with twists,
surgical retractors, MBbius electrical components and train tracks, knot
patents, the metaphysics of shoelaces, chirality, Lipitor, Paxil, Zoloft, Nexium,
thalidomide, Advil, enantiomers, Methanobacterium thermoautotrophicum,
Mobius plant proteins that induce labor in African women, Mobius crystals, the
Noah's ark puzzle, and Mobius strips in fashion and hairstyle.... 39
Strange Adventures in Topology and Beyond
In which we encounter Benoit Mandelbrot, fractals, parameterizations, a con-
ical helix, butterfly curves, paradromic rings, Leonhard Euler, Antoine-Jean
Lhuillier, chromatic numbers, projective planes, the four-color theorem, "The
Island of Five Colors," Mobius's triangulated band, Johann Listing, homeomor-
phisms, ghosts, the fourth dimension, Immanuel Kant, Johann Carl Friedrich
Zollner, Henry Slade, Alfred Schofield's "Another World," turning spheres and
doughnuts inside out, optiverses, the Boy surface, cross-caps, Roman sur-
faces, the fantastic Mobius function, the Mertens conjecture, the Riemann
zeta function, Mobius palindromes, the amazing n, coprimality, graph theory,
hexaflexagons, Mobius shorts, Mobius tetrahedra, Mobius triangles, solenoids,
Alexander's horned sphere, prismatic doughnuts, perfect square dissections,
the squiggle map coloring puzzle, the cannibal torus, the pyramid puzzle, and
Mobius in pop culture.... 61
Cosmos, Reality, Transcendence
In which we encounter nonorientable spaces, more enantiomorphs, dextro-
cardia with situs inversus, hyperspheres, Klein bottle coffee mugs, the world's
largest Klein bottle, the Bonan-Jeener's Klein surface, Immanuel Kant redux,
bilaterally symmetric Vernanimalcula guizhouena, the Babylonian god
Marduk, Gottfried Wilhelm Leibniz, 3-tori, Max Tegmark, parallel universes,
artificial life, simulated universes, John Horton Conway, the Wilkinson
Microwave Anisotropy Probe, Gerardus Mercator, the ekpyrotic model of uni-
verse formation and destruction, the book of Genesis, self-reproducing uni-
verses, playing God, the pretzel transformation puzzle, and Mbbius
cosmoses.... 111
Games, Mazes, Art, Music, and Architecture
In which we encounter Mobius chess, mazes, knight's tours, bishop domina-
tion on a Klein bottle chessboard, Mbbius stairs and snow sculptures, Mobius
buildings, Mobius postage stamps, Max Bill, Lego sculptures beyond imagina-
tion, M6bius gear assemblies, complex knots, Teja Krasek, MBbius strips with
Penrose tilings, Mobius music, Johann Sebastian Bach, Arnold Schoenberg,
Nicolas Slonimsky, devil configurations, Mobius strips in psychology and
human relations, and mazes played on M6bius strips.... 145
Literature and Movies
In which we encounter the literature of nonorientable surfaces, the "No-Sided
Professor," "A. Botts and the Mobius Strip," "Paul Bunyon Versus the Conveyor
Belt," "The Wall of Darkness," "A Subway Named Mobius," Gustavo Mosquera,
The Secret Life of Amanda K. Woods, The Journey of MObius and Sidh, The
Lobotomy Club, Flatterland, Bana Witt's Mobius Stripper, Dhalgren, Marcel
Proust's In Search of Lost Time, Six Characters in Search of an Author, Time
and the Conways, Donnie Darko, Femme Fatale, Mobius the Stripper, Vladimir
Nabokov's The Gift, Coleman Dowell's island People, Daniel Hayes's Tearjerker,
Eugene lonesco's The Bald Soprono, Solvej Balle's According to the Law, John
Barth's Lost in the Funhouse, Paul Nahin's "Twisters," Martin Gardner's Visitors
from Oz, ants trapped in Jordan curves, and Mobius in the suburbs.... 173
A Few Final Words
In which we encounter Stanislaw Ulam, Franz Reuleaux, Georg Bernhard Rie-
mann, Zen koans, Eternal Sunshine of the Spotless Mind, Harlan Brothers, Mar-
jorie Rice, Roger Penrose, Arthur C. Clarke, the Mandelbrot set, an ambiguous
ring, and Mobius strips in business and government. 191