Pickover C.A. The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

Sterling, 2009. — 528 p. — (Sterling Milestones). — ISBN 9781402757969, 1402757964.Math’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.Introduction.
c. 150 Million B.C. Ant Odometer.
c. 30 Million B.C. Primates Count.
c. 1 Million B.C. Cicada-Generated Prime Numbers.
c. 100,000 B.C. Knots.
c. 18,000 B.C. Ishango Bone.
c. 3000 B.C. Quipu.
c. 3000 B.C. Dice.
c. 2200 B.C. Magic Squares.
c. 1800 B.C. Plimpton 322.
c. 1650 B.C. Rhind Papyrus.
c. 1300 B.C. Tic Tac Toe.
c. 600 B.C. Pythagorean Theorem and Triangles.
548 B.C. Go.
c. 530 B.C. Pythagoras Founds Mathematical Brotherhood.
c. 445 B.C. Zeno’s Paradoxes.
c. 440 B.C. Quadrature of the Lune.
c. 350 B.C. Platonic Solids.
c. 350 B.C. Aristotle’s Organon.
c. 320 B.C. Aristotle’s Wheel Paradox.
300 B.C. Euclid’s Elements.
c. 250 B.C. Archimedes: Sand, Cattle & Stomachion.
c. 250 B.C. π.
c. 240 B.C. Sieve of Eratosthenes.
c. 240 B.C. Archimedean Semi-Regular Polyhedra.
225 B.C. Archimedes’ Spiral.
c. 180 B.C. Cissoid of Diocles.
c. 150 Ptolemy’s Almagest.
250 Diophantus’s Arithmetica.
c. 340 Pappus’s Hexagon Theorem.
c. 350 Bakhshali Manuscript.
415 The Death of Hypatia.
c. 650 Zero.
c. 800 Alcuin’s Propositiones ad Acuendos Juvenes.
830 Al-Khwarizmi’s Algebra.
834 Borromean Rings.
850 Ganita Sara Samgraha.
c. 850 Thabit Formula for Amicable Numbers.
c. 953 Chapters in Indian Mathematics.
1070 Omar Khayyam’s Treatise.
c. 1150 Al-Samawal’s The Dazzling.
c. 1200 Abacus.
1202 Fibonacci’s Liber Abaci.
1256 Wheat on a Chessboard.
c. 1350 Harmonic Series Diverges.
c. 1427 Law of Cosines.
1478 Treviso Arithmetic.
c. 1500 Discovery of Series Formula for π.
1509 Golden Ratio.
1518 Polygraphiae Libri Sex.
1537 Loxodrome.
1545 Cardano’s Ars Magna.
1556 Sumario Compendioso.
1569 Mercator Projection.
1572 Imaginary Numbers.
1611 Kepler Conjecture.
1614 Logarithms.
1621 Slide Rule.
1636 Fermat’s Spiral.
1637 Fermat’s Last Theorem.
1637 Descartes’ La Géométrie.
1637 Cardioid.
1638 Logarithmic Spiral.
1639 Projective Geometry.
1641 Torricelli’s Trumpet.
1654 Pascal’s Triangle.
1657 The Length of Neile’s Semicubical Parabola.
1659 Viviani’s Theorem.
c. 1665 Discovery of Calculus.
1669 Newton’s Method.
1673 Tautochrone Problem.
1674 Astroid.
1696 L’Hôpital’s Analysis of the Infinitely Small.
1702 Rope around the Earth Puzzle.
1713 Law of Large Numbers.
1727 Euler’s Number, e.
1730 Stirling’s Formula.
1733 Normal Distribution Curve.
1735 Euler-Mascheroni Constant.
1736 Königsberg Bridges.
1738 St. Petersburg Paradox.
1742 Goldbach Conjecture.
1748 Agnesi’s Instituzioni Analitiche.
1751 Euler’s Formula for Polyhedra.
1751 Euler’s Polygon Division Problem.
1759 Knight’s Tours.
1761 Bayes’ Theorem.
1769 Franklin Magic Square.
1774 Minimal Surface.
1777 Buffon’s Needle.
1779 Thirty-Six Officers Problem.
c. 1789 Sangaku Geometry.
1795 Least Squares.
1796 Constructing a Regular Heptadecagon.
1797 Fundamental Theorem of Algebra.
1801 Gauss’s Disquisitiones Arithmeticae.
1801 Three-Armed Protractor.
1807 Fourier Series.
1812 Laplace’s Théorie Analytique des Probabilités.
1816 Prince Rupert’s Problem.
1817 Bessel Functions.
1822 Babbage Mechanical Computer.
1823 Cauchy’s Le Calcul Infinitésimal.
1827 Barycentric Calculus.
1829 Non-Euclidean Geometry.
1831 Möbius Function.
1832 Group Theory.
1834 Pigeonhole Principle.
1843 Quaternions.
1844 Transcendental Numbers.
1844 Catalan Conjecture.
1850 The Matrices of Sylvester.
1852 Four-Color Theorem.
1854 Boolean Algebra.
1857 Icosian Game.
1857 Harmonograph.
1858 The Möbius Strip.
1858 Holditch’s Theorem.
1859 Riemann Hypothesis.
1868 Beltrami’s Pseudosphere.
1872 Weierstrass Function.
1872 Gros’s Théorie du Baguenodier.
1874 The Doctorate of Kovalevskaya.
1874 Fifteen Puzzle.
1874 Cantor’s Transfinite Numbers.
1875 Reuleaux Triangle.
1876 Harmonic Analyzer.
1879 Ritty Model I Cash Register.
1880 Venn Diagrams.
1881 Benford’s Law.
1882 Klein Bottle.
1883 Tower of Hanoi.
1884 Flatland.
1888 Tesseract.
1889 Peano Axioms.
1890 Peano Curve.
1891 Wallpaper Groups.
1893 Sylvester’s Line Problem.
1896 Proof of the Prime Number Theorem.
1899 Pick’s Theorem.
1899 Morley’s Trisector Theorem.
1900 Hilbert’s 23 Problems.
1900 Chi-Square.
1901 Boy’s Surface.
1901 Barber Paradox.
1901 Jung’s Theorem.
1904 Poincaré Conjecture.
1904 Koch Snowflake.
1904 Zermelo’s Axiom of Choice.
1905 Jordan Curve Theorem.
1906 Thue-Morse Sequence.
1909 Brouwer Fixed-Point Theorem.
1909 Normal Number.
1909 Boole’s Philosophy and Fun of Algebra.
1910–1913 Principia Mathematica.
1912 Hairy Ball Theorem.
1913 Infinite Monkey Theorem.
1916 Bieberbach Conjecture.
1916 Johnson’s Theorem.
1918 Hausdorff Dimension.
1919 Brun’s Constant.
c. 1920 Googol.
1920 Antoine’s Necklace.
1921 Noether’s Idealtheorie.
1921 Lost in Hyperspace.
1922 Geodesic Dome.
1924 Alexander’s Horned Sphere.
1924 Banach-Tarski Paradox.
1925 Squaring a Rectangle.
1925 Hilbert’s Grand Hotel.
1926 Menger Sponge.
1927 Differential Analyzer.
1928 Ramsey Theory.
1931 Gödel’s Theorem.
1933 Champernowne’s Number.
1935 Bourbaki: Secret Society.
1936 Fields Medal.
1936 Turing Machines.
1936 Voderberg Tilings.
1937 Collatz Conjecture.
1938 Ford Circles.
1938 The Rise of Randomizing Machines.
1939 Birthday Paradox.
c. 1940 Polygon Circumscribing.
1942 Hex.
1945 Pig Game Strategy.
1946 ENIAC.
1946 Von Neumann’s Middle-Square Randomizer.
1947 Gray Code.
1948 Information Theory.
1948 Curta Calculator.
1949 Császár Polyhedron.
1950 Nash Equilibrium.
c. 1950 Coastline Paradox.
1950 Prisoner’s Dilemma.
1952 Cellular Automata.
1957 Martin Gardner’s Mathematical Recreations.
1958 Gilbreath’s Conjecture.
1958 Turning a Sphere Inside Out.
1958 Platonic Billiards.
1959 Outer Billiards.
1960 Newcomb’s Paradox.
1960 Sierpinski Numbers.
1963 Chaos and the Butterfly Effect.
1963 Ulam Spiral.
1963 Continuum Hypothesis Undecidability.
c. 1965 Superegg.
1965 Fuzzy Logic.
1966 Instant Insanity.
1967 Langlands Program.
1967 Sprouts.
1968 Catastrophe Theory.
1969 Tokarsky’s Unilluminable Room.
1970 Donald Knuth and Mastermind.
1971 Erdös and Extreme Collaboration.
1972 HP-35: First Scientific Pocket Calculator.
1973 Penrose Tiles.
1973 Art Gallery Theorem.
1974 Rubik’s Cube.
1974 Chaitin’s Omega.
1974 Surreal Numbers.
1974 Perko Knots.
1975 Fractals.
1975 Feigenbaum Constant.
1977 Public-Key Cryptography.
1977 Szilassi Polyhedron.
1979 Ikeda Attractor.
1979 Spidrons.
1980 Mandelbrot Set.
1981 Monster Group.
1982 Ball Triangle Picking.
1984 Jones Polynomial.
1985 Weeks Manifold.
1985 Andrica’s Conjecture.
1985 The ABC Conjecture.
1986 Audioactive Sequence.
1988 Mathematica.
1988 Murphy’s Law and Knots.
1989 Butterfly Curve.
1996 The On-Line Encyclopedia of Integer Sequences.
1999 Eternity Puzzle.
1999 Perfect Magic Tesseract.
1999 Parrondo’s Paradox.
1999 Solving of the Holyhedron.
2001 Bed Sheet Problem.
2002 Solving the Game of Awari.
2002 Tetris Is NP-Complete.
2005 NUMB3RS.
2007 Checkers Is Solved.
2007 The Quest for Lie Group E8.
2007 Mathematical Universe Hypothesis.
Notes and Further Reading.
Index.
Photo Credits.
About the Author.