The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of MathematicsMath’s infinite mysteries and beauty unfold in this follow-up to the best-selling The Science Book. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.
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Contents
Introduction | 10 |
B C Go | 42 |
B C Euclids Elements | 56 |
B C Archimedes Spiral | 66 |
Slide Rule | 130 |
Fermats Spiral | 132 |
Fermats Last Theorem | 134 |
Descartes La Géométrie | 136 |
Babbage Mechanical Computer | 218 |
Cauchys Le Calcul Infinitésimal | 220 |
Barycentric Calculus | 222 |
NonEuclidean Geometry | 224 |
Möbius Function | 226 |
Group Theory | 228 |
Pigeonhole Principle | 230 |
Quaternions | 232 |
Cardioid | 138 |
Logarithmic Spiral | 140 |
Projective Geometry | 142 |
Torricellis Trumpet | 144 |
Pascals Triangle | 146 |
The Length of Neiles Semicubical Parabola | 148 |
Vivianis Theorem | 150 |
Discovery of Calculus | 152 |
Newtons Method | 154 |
Tautochrone Problem | 156 |
Astroid | 158 |
LHôpitals Analysis of the Infinitely Small | 160 |
Rope around the Earth Puzzle | 162 |
Law of Large Numbers | 164 |
Eulers Number e | 166 |
Stirlings Formula | 168 |
Normal Distribution Curve | 170 |
EulerMascheroni Constant | 172 |
Königsberg Bridges | 174 |
St Petersburg Paradox | 176 |
Goldbach Conjecture | 178 |
Agnesis Instituzioni Analitiche | 180 |
Eulers Formula for Polyhedra | 182 |
Eulers Polygon Division Problem | 184 |
Knights Tours | 186 |
Bayes Theorem | 188 |
Franklin Magic Square | 190 |
Minimal Surface | 192 |
Buffons Needle | 194 |
ThirtySix Officers Problem | 196 |
Sangaku Geometry | 198 |
Least Squares | 200 |
Constructing a Regular Heptadecagon | 202 |
Fundamental Theorem of Algebra | 204 |
Gausss Disquisitiones Arithmeticae | 206 |
ThreeArmed Protractor | 208 |
Fourier Series | 210 |
Laplaces Théorie Analytique des Probabilités | 212 |
Prince Ruperts Problem | 214 |
Bessel Functions | 216 |
Transcendental Numbers | 234 |
Catalan Conjecture | 236 |
The Matrices of Sylvester | 238 |
FourColor Theorem | 240 |
Boolean Algebra | 242 |
Icosian Game | 244 |
Harmonograph | 246 |
The Möbius Strip | 248 |
Holditchs Theorem | 250 |
Riemann Hypothesis | 252 |
Beltramis Pseudosphere | 254 |
Weierstrass Function | 256 |
Gross Théorie du Baguenodier | 258 |
The Doctorate of Kovalevskaya | 260 |
Reuleaux Triangle | 266 |
Venn Diagrams | 272 |
Tower of Hanoi | 278 |
Peano Axioms | 284 |
Sylvesters Line Problem | 290 |
Morleys Trisector Theorem | 296 |
Boys Surface | 302 |
Poincaré Conjecture | 308 |
Jordan Curve Theorem | 314 |
Normal Number | 320 |
Hairy Ball Theorem | 326 |
Information Theory | 394 |
Nash Equilibrium | 400 |
Cellular Automata | 406 |
Turning a Sphere Inside Out | 412 |
Sierpiński Numbers | 420 |
Continuum Hypothesis Undecidability | 426 |
Mandelbrot Set | 472 |
Jones Polynomial | 478 |
The ABC Conjecture | 484 |
Murphys Law and Knots | 490 |
Eternity Puzzle | 496 |
Solving of the Holyhedron | 502 |
Notes and Further Reading | 518 |
526 | |
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Common terms and phrases
Algebra Andrica's Conjecture Archimedes arithmetic ball behavior Brun's Constant calculations century Cicada-Generated Prime Numbers circle colors construct created cube curve Descartes digits dimensions discovered discovery Disquisitiones Arithmeticae Elements 300 B.C. equations Erdös Euclid's Elements 300 Euler's example exist famous Fermat finite formula fractal French mathematician function Gauss geometry German mathematician Gilbreath's Conjecture graph Hilbert's Grand Hotel Icosian imaginary numbers infinite number integers Klein Bottle knots Laplace's Théorie Analytique Large Numbers Leonhard Logarithmic magic square Mandelbrot Martin Gardner Math mathematician mathematics Million B.C. Möbius Strip Newcomb's Paradox number theory objects patterns Peano Penrose Tiles physicist Pickover plane Platonic Solids player polygon Polyhedra polynomial probability problems proof proved published puzzle Pythagorean real numbers Riemann Hypothesis scientists sequence shape solution solve sphere Spidrons surface symmetry Szilassi Polyhedron tesseract Today Transfinite Numbers triangle Ulam Spiral University visualize writes wrote zero