Edward Kasner (1878–1955)

Indeholder "Introduction", "1. New Names for Old", " Easy words for hard ideas", " Transcendental", " Non-simple 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", " Notes", "2. Beyond the Googol", " 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 zero", " 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", " Notes", "3. PIE (π, i, e) - Transcendental and Imaginary", " Chinamen and chandeliers", " Twilight of common sense", " π, 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 π", " 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 sqrt(-1), or 'Where am I?'", " Biography of i, the self-made amphibian", " Omar Khayyám, 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", " Notes", "4. Assorted Geometries, Plane and Fancy", " 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", " Notes", "5. Pastimes of Past and Present Times", " 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", " Notes", "6. Paradox Lost and Paradox Regained", " 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 mathematics do?", " Notes", "7. Chance and Chanceability", " 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 stand-by", " Mr. Socrates may not die", " Ring out the old logic, ring in the new", " Notes", "8. Rubber-sheet Geometry", " 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", " Old 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 Möbius 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 ", " Notes", "9. Change and Changeability", " 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 integral", " Indefinite integral", " One the inverse of the other", " The outline of history and the descent of man: or, y=e^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 unbelievable crisscross", " Notes", "Epilogue. Mathematics and the Imagination", "Bibliography", "Index".

Bogen var en bestseller i sin tid og er første gang ordet Googol optræder på tryk (1949). Den når rundt om helt utroligt mange emner, men lidt for elementært til at fange interessen i længere tid.… (meer)