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A Passion for Mathematics
Numbers, Puzzles, Madness, Religion,and the Quest for Reality
Mathematics is the hammer
Numbers percolate like bubbles in the ocean of mathematics.
Math puzzles, factoids, quotations, trivia, formulas... Click here to see the book at Amazon.Com 
A Smorgasbord of math puzzles, factoids, quotations, trivia, formulas, and much more...Are you fascinated by numbers and want to learn more? Does the vast world of math problems that humans have solved—and the ones we have yet to begin to comprehend—give you goose bumps? If so, this is the book for you. A Passion for Mathematics is an educational, entertaining trip through the curiosities of the math world, blending an eclectic mix of history, biography, philosophy, number theory, geometry, probability, huge numbers, and mindbending problems into a delightfully compelling collection that is sure to please math buffs, students, and experienced mathematicians alike.
In each chapter, Clifford Pickover provides factoids, anecdotes, definitions, quotations, mathematical art, and captivating challenges that range from fun, quirky puzzles to insanely difficult problems. You'll encounter mad mathematicians, strange number sequences, obstinate numbers, curious constants, magic squares, fractal geese, monkeys typing Hamlet, infinity, and much, much more.
If you love all things mathematical, A Passion for Mathematics will feed your fascination while giving your problemsolving skills a great workout!
"A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today." —Journal of Recreational Mathematics
Ramanujan 
A fragment from the Preface of A Passion for Mathematics: "Readers of my popular mathematics books already know how I feel about numbers. Numbers are portals to other universes. Numbers help us glimpse a greater universe normally shielded from our small brains that have not evolved to comprehend fully the mathematical fabric of the universe. Higher mathematical discussions are a little like poetry. Danish physicist Niels Bohr felt similarly about physics when he said, "We must be clear that, when it comes to atoms, language can be used only as in poetry.'"
"When I think about the vast oasis of numbers that humans have skimmed from the shoreless sea of reality, I get a little shiver. I hope you'll shiver too as you glimpse numbers ranging from integers, fractions, and radicals to stranger beasts like the transcendental numbers, transfinite numbers, hyperreal numbers, surreal numbers, the "nimbers," the quaternions, biquaternions, sedenions, and octonions. Of course, we have a hard time thinking of such queer entities, but from time to time, God places in our midst visionaries who function like the Biblical prophets who touched a universe inches away that most of us can barely perceive." 
Mathematical Marvels from Beyond the Edge
The Ramanujan Code
Blood Dreams and God's Mathematicians
The Mathematical Smorgasbord
Explanation of Symbols
Cultivating Perpetual Mystery
In which we encounter religious mathematicians, mad mathematicians, famous mathematicians, mathematical savants, quirky questions, fun trivia, brief biographies, mathematical gods, historical oddities, numbers and society, gossip, the history of mathematical notation, the genesis of numbers, and "what if?" questions. Do humans invent mathematics or discover mathematics? What is reality? Why does the universe seem to operate according to mathematical laws? What is the most forgettable license plate? Which brilliant mathematicians were mass murderers? What is Ramanujan's tongue? Why was the first woman mathematician murdered? When was the multiply symbol first actually used in a book? Who was the "Number Pope"? Why are there 360 degrees in a circle? Who invented the symbol for infinity? In how many ways can you place Xs and Os on a tic tac toe board? What mathematical genius despised and feared mirrors? What happens when you double the salary of every mathematics teacher? What romantic comedy has the most complicated mathematics ever portrayed in a movie? What number is on Agent Smith's license plate in the movie Matrix Reloaded, and why? What is the earliest evidence we have of humans counting? Can animals count? Which mathematicians claimed that their mathematical breakthroughs came directly from God? What was the largest number ever used in the title of an American movie? Why is there no Nobel Prize for Mathematics? How much mathematics can we know? Does God exist?
In which we encounter fascinating numbers and strange number sequences. We'll explore transcendental numbers, octonions, surreal numbers, obstinate numbers, cyclic numbers, Vibonacci numbers perfect numbers, automorphic numbers, prime numbers, Wilson primes, palindromic primes, Fibonacci primes, Sophie Germain primes, BaxterHickerson primes, starcongruent primes, narcissistic numbers, amenable numbers, amicable numbers, padic numbers, large palindromes, factorions, hyperfactorials, primorials, palindions and hyperpalindions, exoticlooking formulas for pi, the GolayRudinShapiro sequence, wonderful Pochhammer notation, famous and curious math constants (like Liouville's constant, the CopelandErdös constant, Brun's constant, Champernowne's number, Euler's gamma, Chaitin's constant, the LandauRamanujan constant, Mill's constant, the golden ratio, Apéry's constant, and constants even more bizarre)... Who discovered pi? What are "nimbers"? What would happen if everyone's body weight were quantized and came in multiples of pi pounds? Could Jesus of Nazareth ever have worked with a negative number, like 3? Could Jesus multiply two numbers? Is it true that we all live happy lives, coded in the endless digits of pi? Why is the number 13 considered unlucky?
In which we encounter treasure chests of zany and educational math problems involving algebra, fractions, percentages, classic recreational puzzles, and various mathematical manipulation. Some are based on problems over a thousand years old. Others are brand new. Get ready to sharpen your pencils and stretch your brains! Can you show why x^0 = 1? What is a fragile fraction? What is a hyperpower tower? The doomsday formula? The Riemann hypothesis? Are there difficult math problems lurking in the ancient Indian sex manual, The Kama Sutra? Experiment with puzzles involving alien ships, lying robots, sparkling angels, wealthy jewelers, wizards, Martians, alien spheres, the spread of disease, the liquefaction of human flesh, bacterial growth, extraterrestrial slugs, the Bakhshali manuscript, and the Leaning Tower of Pisa.
In which we explore tiles, patterns, position problems, arrays, Venn diagrams, tic tac toe, other games played on boards, Königsberg bridges, catenaries, Loyd's and Dudeney's puzzles, Sherck's surface, magic squares, lituuses, insideout Mandelbrot sets, the Quadratrix of Hippias, hyperspheres, fractal geese, Schmidhuber circles, Pappus' Arbelos, Escher patterns, and chess Knights. Would you like to live in a house shaped like a torus? If everyone on Earth stood on his own 3by3 foot piece of ground, how large an area would humanity cover? Is the universe shaped like a dodecahedron? Would it be possible to cram a polar bear into an 11dimensional sphere with a 6inch radius? What is a golygon? The mysterious sangaku or the Stomachion of Archimedes? The Lute of Pythagoras? Fractal froth? Osculating circles? Explore The Simpsons and geometry, exotic chess games, strange spirals, caterpillar planets, Jordan curves, alien colonies,Möbius mirrors, Aesculpian mazes, exploding circles, grids of the gods, Procyon maneuvers, Koch curves, robot worms, Ikeda attractors, loxodromes, Borromean rings, chaos machines, Schoenberg curves, Wither's attractors, zenograms, butterfly curves, Lorenz attractors, Johnson functions, and magic squares.
In which we explore casinos, logic, guessing, decisions, combinations, permutations, competition, possibilities, games involving choice, monkeys typing Hamlet, Benford's law, permutations, combinatorics, alien gambits, Rubik's cubes, card shuffles, marble mazes, nontransitive dice, and dangerous movements of air molecules. How can you instantly turn an unfair coin into a fair one for coin tossing games? What is the probability that you will hit Africa with a dart thrown at a world map? In randomly played tictactoe, what is the chance that the first player wins? In how many different ways can we arrange the 52 cards in a playing card deck? What piano note is a blindfolded person most likely to play when randomly striking a key? How does chance and probability affect the way we look at the world? Play with robot jaws, triangles and spiders, apes in barrels, and men that vaporize you with a touch. Play the board game of the gods and enter the tunnels of death and despair.
In which we explore very large numbers, the edges of comprehension, infinity, the funnel of Zeus, the infinite gift, Skewes' number, the Monster group, Göbel's number, the ErdösMoser number, the awesome quattuordecillion, Archimedes' famous "Cattle Problem," classic paradoxes, Gauss's "measurable infinity," and Knuth's arrow notation. What is the largest number that a future computer could work with or yield as a result of a computation? How many life experiences can a person have? What is the largest known number described in a work of fiction? What is the number of possible chess positions? What is an infinite gift? How large a number is the Buddhist asankhyeya? Just how enormous is 9^9^9? What is an infinity keyboard? How many numbers have a 7 in them? How big is infinity? How large are our minds?
In which we explore artistic forms generated from mathematics  delicate fungi, 22ndcentury cityscapes, fractal necklaces, alien devices, and a rich panoply of forms that exhibit a cascade of detail with increasing magnifications.
AlBattani, 131 Adams, Douglas, 84, 244, 246 Aeon, 244 Agnesi, Maria, 27 AIDS, 219, 349 AlSamawal, 30 Alhazen, 265 algebra, 113, 131 AlKhwarizmi, 131, 282 alphamagic squares, 180 amateur math, 182 annihilation magic square, 180 ant puzzle, 149, 160, 320 antimagic square, 180 Antoine, Louis, 275 apocalyptic magic square, 181 Archimedes, 199, 245 arebelos, 170 arithmetic progressions, 108 arrangements, 213, 214 Asimov, Isaac, 83, 90 attractors, 171,173, 189, 332, 333 Babbage, Charles, 24 Bakhshali problem, 128, 309 Barber paradox, 240 Barrow, John, 252 base, 50 Battles, Zachary , 275 Beal reward, 32 Benford's law, 211 Billion, 47, 277 Bloch, André, 254 Boll, David, 87 Boltzman, Ludwig, 271 book towers, 169, 332 Boole, George, 18 Borromean rings, 171 Bourbaki, N., 39, 271 Brahmagupta, 114 Briffault, Robert, 63 Brothers, Harlan, 76 Buddhist, 244 butterfly curves, 188 calculus, 30, 3435, 267, 308 Cantor, Georg, 24, 216, 237, 238, 260, 327, 362 card arrangements, 217, 229, 348 cardinality, 47, 49 casualty equations, 267 catenary, 142 cattle problem, 245 Chalmers, David, 47 chaos, 190, 333 chess, 143, 144, 145, 185, 195, 196, 197, 198, 199, 217, 247, 340, 347 circles, 16, 146, 154, 159, 164, 165, 170, 172, 193, 203, 206, 254, 317, 324, 329, 330, 333, 334, 350 circular permutations, 213 coin tosses, 211, 227, 228, 342, 355, 358 coincidence, 36, 90, 92, 98, 101 combinatorics, 213, 215 Constantine window puzzle, 203, 342 Constants 0.065988..., 90 0.692200..., 90 1.506592..., 90 1.92878... , 97 Apery's, 90, 359 Brun's, 93 Chaitin, 77 Champernowne, 59, 280 coincidental, 90 CopelandErdös, 60, 280 Euler's gamma, 77, 104, 130 Euler's number, 52, 53, 55, 58, 76, 82, 83, 86, 87, 90, 92, 101, 102, 104, 106, 117, 123, 127, 142, 143, 178, 265, 276, 279, 280, 287, 308, 314, 336 EulerMascheroni, 77, 104 fine structure, 86, 87 golden ratio, 8082, 86, 95, 104, 105, 143, 198, 315 infinite power tower, 90 LandauRamanujan, 101 Liouville, 58, 278, 280 Mandelbrot, 90 Mill's (a), 98 pi, 16, 29, 31, 35, 47, 52, 53, 55, 5860, 62, 72, 75, 7678, 8092, 101, 102, 104106, 109, 143, 147, 182, 256, 265, 270, 276, 277, 279, 280, 283, 286, 287, 292, 294, 314 Thue, 60, 280 continuity, 166, 330, 331 continuum, 48 continuum hypothesis, 237 continuum puzzle, 151, 322 Conway, John, 57, 77, 93, 94, 185, 229 counting, 13, 16, 19, 235, 254, 257 counting and animals, 257 crescent puzzle, 145, 146, 316, 317 Dürer, Albrecht, 179 Dase, Johann, 31 decimation, 359 derivatives, 308 Descartes, René, 24, 132 dice, 222, 352 Diderot, Denis, 30 Diopantus, 258 doomsday equation, 127 Dudeney, Henry, 176, 177, 178, 186, 336 dynamical systems, 332 Dyson, Freeman, 40, 41, 114, 248 Earls, Jason, 107 Education, 43 Edwards, Anthony, 140 Ehrenfest, Paul, 5 Einstein, Albert, 24, 26, 27, 40, 42, 271 Elkies, Noam, 120 ellipse game, 174, 335 entropy, 106 epitaphs, 39 Erdös, Paul, 18, 26, 33, 51, 65, 69, 72, 246, 256, 290 Eschergram, 335 Euclid, 187 Euler, Leonhard, 18, 30, 33, 52, 77, 80, 83, 85, 96, 98, 103, 105, 120, 137, 185, 265, 274, 359 even number, 47, 77 exponential growth, 126, 308 factors, 100, 229 Fermat numbers, 59 Fermat spiral, 169 Fermat, Pierre de, 32, 187, 254 Fermat's Last Theorem, 120 Feynman, Richard, 87 Fibonacci, 49, 50, 66, 71, 73, 95, 98, 107, 212, 287, 291 fifteen puzzle, 147, 317 fine structure constant (a), 86, 87 Ford froth, 163 Fourier, Jean, 263 fractals, 85, 87, 90, 155, 163, 175, 188, 190, 191, 194, 251, 325, 331 caves, 175 drums, 194 geese, 190 swords, 194 The Fractal Murders (novel), 42 Funnel of Zeus, 364 Gödel, Kurt, 22, 41, 248, 258, 259, 269 Gödel's theorem, 259 Gabriel's horn, 364 Galois, Évariste, 266 gambling, 211 game shows, 37, 271 Gamm, Rüdiger, 21 Ganson, Mark, 89, 107, 349 Gardner, John, 275 Gardner, Martin, 94, 162, 183, 219, 251, 274, 275 Gauss, Carl Friedrich, 17, 237, 284 gears, 164, 329 GellMann, Murray, 8 geometry, 135209 Germain, Sophie, 27 Go, 244 Göbel's sequence, 241 GolayRudinShapiro Sequence, 79 Goldbach conjecture, 59 Golygon, 144, 314, 315 googol, 69 googolplex, 236 Gosper, William, 85 Grünbaum, Branko139 graph theory, 137 grasshopper sequences, 68, 289 greatest common divisor, 319 Greek notation, 31 Grim, Patrick, 155, 325 group theory, 266 Guberlet, Constantin, 49 Guy, Richard, 94, 229 Hales, Thomas, 4 Hamburger, Peter, 139 Hankel, Hermann, 33 Harborth configuration, 192 Hardy, G. H., 2, 23, 142, 143, 241, 247, 251, 257, 275, 290 harmonic series, 103, 119, 130, 132, 310, 311 Heisenberg Uncertainty Principle, 82 Heisenberg, Werner, 4 helical curves, 188 Heron's problem, 173, 334 heterosquares, 150, 322 hexgonal cutting, 165 hexcongruent primes, 100 Hilbert, David, 33, 101 hoax, 90, 294 HoënéWronski, Josef, 32 Honaker, G. L., 99, 108, 109 Hypatia, 259 hypercubes, 192, 194 hyperpower towers, 123 hyperpyramids, 195 hyperspheres, 193, 359 Ikeda attractor, 332 infinite series, 102 infinity symbol, 25 infinity keyboard, 365 infinity, 26, 233, 237, 239, 240, 241, 244, 363, 365 infinite product, 103 James, William, 275 Jeans, James, 17 Jefferson, Thomas, 204 Jerusalem crystal puzzle, 205 Jesus, 61, 282 jeweler puzzle, 116 Jews, 35, 270 Jacobs, Bobby, 34 Johnson functions, 198 Johnson's theorem, 317 Jordan curves, 160, 328 Kaczynski, Ted, 261 Kalman, Rudolf, 106 Kama Sutra puzzle, 125, 307 Kant, Immanuel, 14 knight placement, 197, 198, 340 knights tours, 185, 186, 195, 196, 197 Knuth, Donald, 20, 94, 236, 361 Koch curve, 166, 331 Königsberg bridges, 137 Kronecker, Leopold, 51 L'Hôpital, Gillaume de, 35 Lagrange, Joseph, 35, 98 Lanchester, F., 267 large law, 235 Latin squares, 320 lattice numbers, 196, 339 least common multiple, 302 Lego sequence, 65, 287 Leibniz, Gottfried, 22, 34, 36, 267, 277 license plates, 16, 36, 255 limit, 167, 332 Liouville, Joseph, 58 lituus, 187 Lobachevsky, Nikolai, 36, 144 Lorenz attractor, 189 lost in hyperspace, 150, 321 LotkaVolterra equations, 267 love formulas, 129 Lovelace, Ada, 264 loxodrome, 170 Loyd, Sam, 7, 113, 114, 115, 145, 146, 147, 295, 296, 297, 317 lute of Pythagoras, 204, 315 lyrics, song, 270 MacArthur awards, 41, 48 magic squares, 56, 57, 150, 153, 154, 179184, 195, 278, 321, 324 magic circles, 165, 329 magic spheres, 166, 330 Mahavira problem, 127, 308 Mandelbrot set, 85, 87, 90, 188, 191, 251, 252 map coloring, 207 map projections, 345 Mathematicians blind, 42, 274 epitaphs, 39, 271 first, 37 homosexual, 26, 257 madness and creativity, 14, 23, 26, 39, 260, 263 mirror phobic, 257 murderers, 25, 254, 261 murdered, 259 number Pope, 23 prolific, 28, 33 religious, 14,15, 17, 18, 2024, 37, 38, 265 savants, 21, 31, 34 starving, 258 women, 22, 26, 27, 28, 259, 263, 264 Mathematics beauty, 13, 239 computers, 4 dreams, 15 education, 43, 263, 275 Jews, 35, 73, 270 game shows, 37 God and religion, 3, 14, 15, 17, 18, 2325, 27, 28, 30, 31, 33, 34, 50, 74, 80, 83, 143, 235, 238, 254, 260, 261, 269, 272 proofs, 4 mind, 4 movies, 22, 26, 35, 36, 93, 260, 270, 271 novels, 42 nature and cosmos, 8, 13, 30, 42, 50, 52, 84, 162, 183, 198, 223, 247249, 268, 273, 340 plays, 40 predictive power, 8 real world, 8 reality, 13, 30, 40, 41, 43, 220, 226, 229, 249, 251, 268, 273, 275 simultaneity, 36 The Matrix, 2, 36, 271 maze, 161, 214, 215, 328, 345 Mersenne numbers, 19 Mersenne, Marin, 18 mirror phobia, 19, 257 Mirror magic squares, 182 MittagLeffler, Gösta, 272 Möbius strip, 199 molecule puzzle, 202, 341 The Modulor, 2 Mondrian puzzle, 142 monkeys typing Hamlet, 211, 343 moon puzzle, 145, 146, 316, 317 Morin, Bernard, 274 Morse code, 285 MorseThue sequence, 286 Moskowitz, Paul, 255 multiplication principle, 213 murder, 254 Newton, Isaac, 14, 17, 29, 30, 34, 35, 36, 265, 267, 271 Nobel Prize, 40, 272 Nobl, George, 119, 301 Noether, Emmy, 27 nontransitive dice, 222, 352 Notation good notation, 169 Greek, 31 bases, 50 Knuth, 236, 361 Pochhammer, 106 See also symbols number theory, 49 number Pope, 23 Numbers 153, 6869, 289 216, 270 666, 74, 75, 90, 91, 92, 109 abundant, 280 algebraic, 48, 54 almost integers, 85, 87, 90, 294 amenable, 88 ammicable, 93 apocalypic Fibonacci, 73 Armstrong, 289 asankhyeya, 243 augmented primes, 61, 281 automorphic, 264, 287 BaxterHickerson prime, 109 billion, 47, 277 biquaternions, 48, 57 cardinal, 47, 49, 260 catalan, 71 complex, 48, 53, 54, 95 composite, 51, 96 congruent primes, 99, 100 continued fractions, 75, 314 coprime, 75, 91 cube, 9193, 119, 294, 295, 302 cyclic, 89 decillion, 236 diagram, 48, 54 emirp, 73 ErdösMoser, 246 even, 47, 277 exclusionary squares, 60, 281 factorial, 92, 104, 247 factorions, 68, 289 father prime, 89 Fibonacci, 49, 50, 66, 71, 73, 95, 98, 107, 212, 287, 296 Fibonacci prime, 98 fractions, 48, 115, 297, 314 fragile fractions, 115, 297 Göbel's, 241 googol, 69 googolplex, 236 Graham's, 361 Hamiltonian integers, 48, 55 hexcongruent primes, 100 hypercomplex, 48, 54, 55 hyperfactorial, 92 hyperimaginary, 201 hyperpalindion, 107 hyperpower towers, 123 hyperreal, 48, 95 integers, 47, 48, 49, 51, 58 irrational, 48, 54, 70, 72, 291, 293, 327 isoprimes, 60, 97, 281 kinky, 242 large, 234 legion's, 109 leviathan, 243 Mersenne, 19 narcissistic, 289 natural, 48, 54 nimbers, 48, 57 novemdecillion, 236 obstinate, 62, 284 octonions, 48, 55, 57 ordinal, 260 padic, 95 palindions, 107 palindromes, 70, 71, 92, 107, 291 palindromic primes, 97, 108, 109 palinpoints, 66, 288 perfect, 73, 74, 240 prime, 19, 49, 50, 51, 60, 61, 74, 75, 77, 78, 79, 80, 83, 86, 88, 89, 92, 93, 96, 97, 98, 99, 100, 103, 104, 108, 109, 110, 183, 184, 281, 287, 288, 295 primorial prime, 92 pyramidal, 67 quaternions, 48, 54, 55 quattuordecillion, 236 radicals, 48, 96, 103, 106, 143, 266 rational, 19, 47, 53, 104, 120, 129, 237, 268, 302, 327, 362 real, 47, 48, 363 relatively prime, 75, 91 repunit primes, 281 Roman, 40 round, 99 scalar, 54 sedenions, 48, 55, 56 sextillion, 236 skewes, 241 Sopie Germaine prime, 98 square, 68, 70, 92, 98, 281, 291, 294 starcongruent primes, 99 superfactorial, 247 surreal, 48, 93, 94 taxicab, 58, 279 transcendental, 48, 5355, 58, 279, 280 transfinite, 47, 260 transionic, 248 triangular, 78, 91, 92, 288 twin primes, 93 ultrahex, 235, 360 undulating, 50, 62, 80, 284, 289 untouchable, 65, 287 undulating primes, 80 vampire, 287 vibonacci, 107 vigintillion, 236 Wilson prime, 97 zebra, 102 zerofree, 109 osculatory packing, 334 Pagels, Heinz, 113 Pappus' Arbelos, 170 parabolic spiral, 169 paradoxes, 58, 240, 248, 279 parallel universes, 31, 268 paraskevidekatriaphobia, 293 Pascal, Blaise, 14, 15, 36, 71, 254 Pascal's triangle, 71 Pe, Joseph, 66, 86, 255, 310 pendulums, 190 Penrose, Roger, 251 pentagonal numbers, 286 pentagram, 198 permutations, 213, 215 Perrin sequence, 290 persistence, 288 Pi, pi, living in digits, 62, 283 pimagic squares, 182 pipalindromic prime, 109 See also constants, pi Pincus, Steve, 106 Pisa puzzle, 113, 295 Platonic patent, 200 Platonic solids, 154, 325 plays, 40 Pochhammer notation, 106, 107 polyhedreal universe, 340 Pontryagin, Lev, 274 Pope Sylvester II, 23 Poussin proof, 78 prime numbers, See numbers, prime prime magic square, 183, 184 probability, 209232 proofs, 4 Pythagoras, 24, 3739, 261 Pythagoras, lute, 204, 315 Pythagorean triangle, 187, 287 quadratix of Hippias, 192 radicals, 48, 96, 103, 106, 143, 266 Ramanujan, Srinivasa formulas, v, 76, 82, 85, 100106, 279, 294 life and philosophy, 23, 15, 16, 42, 99101, 108 plays, 40 random chords, 350 random selection, 277278 reality, 13, 30, 40, 41, 43, 220, 226, 229, 249, 251, 268, 273, 275 Ribenboim sequence, 68 Rice, Marjorie, 182 Riemann zeta function, 103, 359 Riemann hypothesis, 130 Riemann, Georg, 21, 130 Rivera, Carlos, 74, 84, 109 Roman numerals, 40, 273 rope puzzle, 153 Rubik's cube, 216, 246 Rupert puzzle, 178, 337 Russell, Bertrand, 18, 141, 169, 248 Safford, Truman, 34 Sallows, Lee, 180 sangaku geometry, 201 Saunderson, Nicholas,274 savants, 21, 31, 34 Scherk's surface, 174 Schmidhuber circles, 206 Schoenberg curves, 173, 175 Schrödinger's wave equation, 40 series indefinitely divergent, 131 geometric, 296 slowgrowing, 120 See also harmonic series set theory, 51 seven, 74 Shandy paradox, 248 Sierpinski, Waclaw, 57 sign language, 62, 284 simultaneity, 36. See also coincidence Soler, Cyril, 90 spacefilling curves, 175 spirals, 81, 169, 171, 187, 188 St. Denis, Paul, 155, 325 star, 198 starcongruent primes, 99 Stirling's formula, 104 stomachion, 199 Streisand, Barbra, 93 string theory, 70 students, 134 stylometry, 229, 359 Sumerians, 50, 254 symbols (history of) +, 13, 29 , 13 ÷, 20 > and <, 22 m, 22 ! (factorial), 40 ş, 25, 262 Ĺ, 25 e, 265 ±, 47, 260 pi, 265, 276 calculus, 35 numbers, 32, 34 power notation, 24 variables, 132 synchronicity. See also coincidence talisman square, 154, 324 tea puzzle, 115, 297 teacher puzzle, 114, 296 Tegmark, Mark, 247, 268 Thébault construction, 173 tictactoe, 25, 141143, 145, 155, 211, 223, 262, 325, 352 Tinkertoy computer, 24 toilet paper, 144, 162 Tolstoy, Leo, 92 tori, 145, 146, 316 Torricelli's trumpet, 364 transfinite numbers, 47 triangle of Gods, 61, 282 Tritar, 201 Unabomber, 261 Urantia, 34 Vampire numbers, 287 Venn diagrams, 138 140, 312 Viswanath, Divakar, 107 Vos Savant, Marilyn, 273 Wafa, Abu'l, 130 Wallis, John, 262 war, 185 Wigner, Eugene, 42 Wilson's theorem, 96 Wither's attractor, 173 Yates, Samuel, 100 Yuki Pomo, 50 zenogram, 177 zero, 47 zeta function, 103, 359