| Introduction | |
| New Names for Old | p. 3 |
| Easy words for hard ideas | |
| Transcendental | |
| Nonsimple curve | |
| Simple curve | |
| Simple group | |
| Bolsheviks and giraffes | |
| Turbines | |
| Turns and slides | |
| Circles and cycles | |
| Patho-circles | |
| Clocks | |
| Hexagons and parhexagons | |
| Radicals, hyperradicals, and ultraradicals (nonpolitical) | |
| New numbers for the nursery | |
| Googol and googolplex | |
| Miracle of the rising book | |
| The mathescope | |
| Beyond the Googol | p. 27 |
| Counting--the language of number | |
| Counting, matching, and "Going to Jerusalem" | |
| Cardinal numbers | |
| Cosmic chess and googols | |
| The sand reckoner | |
| Mathematical induction | |
| The infinite and its progeny | |
| Zeno | |
| Puzzles and quarrels | |
| Bolzano | |
| Galileo's puzzle | |
| Cantor | |
| Measuring the measuring rod | |
| The whole is no greater than some of its parts | |
| The first transfinite--Aleph[subscript 0] | |
| Arithmetic for morons | |
| Common sense hits a snag | |
| Cardinality of the continuum | |
| Extravagances of a mathematical madman | |
| The tortoise unmasked | |
| Motionless motion | |
| Private life of a number | |
| The house that Cantor built | |
| [pi], i, e (Pie) | p. 65 |
| Chinamen and chandeliers | |
| Twilight of common sense | |
| [pi], i, e | |
| Squaring the circle and its cousins | |
| Mathematical impossibility | |
| Silk purse, sow's ear, ruler and compass | |
| Rigor mortis | |
| Algebraic equations and transcendental numbers | |
| Galois and Greek epidemics | |
| Cube duplicators and angle trisectors | |
| Biography of [pi] | |
| Infancy: Archimedes, the Bible, the Egyptians | |
| Adolescence: Vieta, Van Ceulen | |
| Maturity: Wallis, Newton, Leibniz | |
| Old Age: Dase, Richter, Shanks | |
| Victim of schizophrenia | |
| Boon to insurance companies | |
| (e) | |
| Logarithms or tricks of the trade | |
| Mr. Briggs is surprised | |
| Mr. Napier explains | |
| Biography of e; or e, the banker's boon | |
| Pituitary gland of mathematics: the exponential function | |
| (i) | |
| Humpty Dumpty, Doctor of Semantics | |
| Imaginary numbers | |
| The [square root]1, or "Where am I?" | |
| Biography of i, the self-made amphibian | |
| Omar Khayyam, Cardan, Bombelli, and Gauss | |
| I and Soviet Russia | |
| Program music of mathematics | |
| Breakfast in bed; or, How to become a great mathematician | |
| Analytic geometry | |
| Geometric representation of i | |
| Complex plane | |
| A famous formula, faith, and humility | |
| Assorted Geometries--Plane and Fancy | p. 112 |
| The talking fish and St. Augustine | |
| A new alphabet | |
| High priests and mumbo jumbo | |
| Pure and applied mathematics | |
| Euclid and Texas | |
| Mathematical tailors | |
| Geometry--a game | |
| Ghosts, table-tipping, and the land of the dead | |
| Fourth-dimension flounders | |
| Henry More to the rescue | |
| Fourth dimension--a new gusher | |
| A cure for arthritis | |
| Syntax suffers a setback | |
| The physicist's delight | |
| Dimensions and manifolds | |
| Distance formulae | |
| Scaling blank walls | |
| Four-dimensional geometry defined | |
| Moles and tesseracts | |
| A four-dimensional fancy | |
| Romance of flatland | |
| Three-dimensional cats and two-dimensional kings | |
| Gallant Gulliver and the gloves | |
| Beguiling voices and strange footprints | |
| Non-Euclidean geometry | |
| Space credos and millinery | |
| Private and public space | |
| Rewriting our textbooks | |
| The prince and the Boethians | |
| The flexible fifth | |
| The mathematicians unite--nothing to lose but their chains | |
| Lobachevsky breaks a link | |
| Riemann breaks another | |
| Checks and double checks in mathematics | |
| The tractrix and the pseudosphere | |
| Great circles and bears | |
| The skeptic persists--and is stepped on | |
| Geodesics | |
| Seventh Day Adventists | |
| Curvature | |
| Lobachevskian Eiffel Towers and Riemannian Holland Tunnels | |
| Pastimes of Past and Present Times | p. 156 |
| Puzzle acorns and mathematical oaks | |
| Charlemagne and crossword puzzles | |
| Mark Twain and the "farmer's daughter" | |
| The syntax of puzzles | |
| Carolyn Flaubert and the cabin boy | |
| A wolf, a goat, and a head of cabbage | |
| Brides and cuckolds | |
| I'll be switched | |
| Poisson, the misfit | |
| High finance; or, The international beer wolf | |
| Lions and poker players | |
| The decimal system | |
| Casting out nines | |
| Buddha, God, and the binary scale | |
| The march of culture; or, Russia, the home of the binary system | |
| The Chinese rings | |
| The tower of Hanoi | |
| The ritual of Benares: or, Charley horse in the Orient | |
| Nim, Sissa Ben Dahir, and Josephus | |
| Bismarck plays the boss | |
| The 15 puzzle plague | |
| The spider and the fly | |
| A nightmare of relatives | |
| The magic square | |
| Take a number from 1 to 10 | |
| Fermat's last theorem | |
| Mathematics' lost legacy | |
| Paradox Lost and Paradox Regained | p. 193 |
| Great paradoxes and distant relatives | |
| Three species of paradox | |
| Paradoxes strange but true | |
| Wheels that move faster on top than on bottom | |
| The cycloid family | |
| The curse of transportation; or, How locomotives can't make up their minds | |
| Reformation of geometry | |
| Ensuing troubles | |
| Point sets--the Arabian Nights of mathematics | |
| Hausdorff spins a tall tale | |
| Messrs. Banach and Tarski rub the magic lamp | |
| Baron Munchhausen is stymied by a pea | |
| Mathematical fallacies | |
| Trouble from a bubble; or, Dividing by zero | |
| The infinite--troublemaker par excellence | |
| Geometrical fallacies | |
| Logical paradoxes--the folk tales of mathematics | |
| Deluding dialectics of the poacher and the prince; of the introspective barber; of the number 111777; of this book and Confucius; of the Hon. Bertrand Russell | |
| Scylla and Charybdis; or, What shall poor mathemathics do? | |
| Chance and Chanceability | p. 223 |
| The clue of the billiard cue | |
| A little chalk, a lot of talk | |
| Watson gets his leg pulled by probable inference | |
| Finds it all absurdly simple | |
| Passionate oysters, waltzing ducks, and the syllogism | |
| The twilight of probability | |
| Interesting behavior of a modest coin | |
| Biological necessity and a pair of dice | |
| What is probability? | |
| A poll of views: a meteorologist, a bootlegger, a bridge player | |
| The subjective view--based on insufficient reason, contains an element of truth | |
| The jackasses on Mars | |
| The statistical view | |
| What happens will probably happen | |
| Experimental eurythmics; or, Pitching pennies | |
| Relative frequencies | |
| The adventure of the dancing men | |
| Scheherezade and John Wilkes Booth--a challenge to statistics | |
| The red and the black | |
| Charles Peirce predicts the weather | |
| How far is "away"? | |
| Herodotus explains | |
| The calculus of chance | |
| The benefits of gambling | |
| De Mere and Pascal | |
| Mr. Jevons omits an acknowledgment | |
| The study of craps--the very guide of life | |
| Dice, pennies, permutations, and combinations | |
| Measuring probabilities | |
| D'Alembert drops the ball | |
| Count Buffon plays with a needle | |
| The point | |
| A black ball and a white ball | |
| The binomial theorem | |
| The calculus of probability re-examined | |
| Found to rest on hypothesis | |
| Laplace needs no hypothesis | |
| Twits Napoleon, who does | |
| The Marquis de Condorcet has high hopes | |
| M. le Marquis omits a factor and loses his head | |
| Fourier of the Old Guard | |
| Dr. Darwin of the New | |
| The syllogism scraps a standby | |
| Mr. Socrates may not die | |
| Ring out the old logic, ring in the new | |
| Rubber-Sheet Geometry | p. 265 |
| Seven bridges over a stein of beer | |
| Euler shivers | |
| Is warmed by news from home | |
| Invents topology | |
| Dissolves the dilemma of Sunday strollers | |
| Babies' cribs and Pythagoreans | |
| Talismen and queer figures | |
| Position is everything in topology | |
| Da Vinci and Dali | |
| Invariants | |
| Transformations | |
| The immutable derby | |
| Competition for the caliph's cup; or, Sifting out the suitors by science | |
| Mr. Jordan's theorem | |
| Only seems idiotic | |
| Deformed circles | |
| Odd facts concerning Times Square and a balloonist's head | |
| Eccentric deportment of several distinguished gentlemen at Princeton | |
| Their passion for pretzels | |
| Their delving in doughnuts | |
| Enforced modesty of readers and authors | |
| The ring | |
| Lachrymose recital around a Paris pissoir | |
| "Who staggered how many times around the walls of what?" | |
| In and out the doughnut | |
| Gastric surgery--from doughnut to sausage in a single cut | |
| N-dimensional pretzels | |
| The Mobius strip | |
| Just as black as it is painted | |
| Foments industrial discontent | |
| Never takes sides | |
| Bane of painter and paintpot alike | |
| The iron rings | |
| Mathematical cotillion; or, How on earth do I get rid of my partner? | |
| Topology--the pinnacle of perversity; or, Removing your vest without your coat | |
| Down to earth--map coloring | |
| Four-color problem | |
| Euler's theorem | |
| The simplest universal law | |
| Brouwer's puzzle | |
| The search for invariants | |
| Change and Changeability | p. 299 |
| The calculus and cement | |
| Meaning of change and rate of change | |
| Zeno and the movies | |
| "Flying Arrow" local--stops at all points | |
| Geometry and genetics | |
| The arithmetic men dig pits | |
| Lamentable analogue of the boomerang | |
| History of the calculus | |
| Kepler | |
| Fermat | |
| Story of the great rectangle | |
| Newton and Leibniz | |
| Archimedes and the limit | |
| Shrinking and swelling; or, "Will the circle go the limit?" | |
| Brief dictionary of mathematics and physics | |
| Military idyll; or, The speed of the falling bomb | |
| The calculus at work | |
| The derivative | |
| Higher derivatives and radius of curvature | |
| Laudable scholarship of automobile engineers | |
| The third derivative as a shock absorber | |
| The derivative finds its mate | |
| Integration | |
| Kepler and the bungholes | |
| Measuring lengths; or, The yawning regress | |
| Methods of approximation | |
| Measuring areas under curves | |
| Method of rectangular strips | |
| The definite [function of] | |
| Indefinite [function of] | |
| One the inverse of the other | |
| The outline of history and the descent of man: or, y = e[superscript x] | |
| Sickly curves and orchidaceous ones | |
| The snowflake | |
| Infinite perimeters and postage stamps | |
| Anti-snowflake | |
| Super-colossal pathological specimen--the curve that fills space | |
| The unbelieveable crisscross | |
| Epilogue: Mathematics and the Imagination | p. 357 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
