Index

abacus ref 1, ref 2

abundant numbers ref 1

accountants, dawn of ref 1

Al-Khwarizmi ref 1

Al-Kindi ref 1

Alcuin of York ref 1

Alexandria ref 1

algebra ref 1, ref 2

Boolean ref 1, ref 2

Boolean, as Venn diagram ref 1

and geometry ref 1

algorithms ref 1

alien civilizations ref 1

Analytical Engine ref 1

Ancient Egypt ref 1, ref 2, ref 3, ref 4

fractions used by ref 1

Ancient Greeks ref 1

alphabet of ref 1

lasting mathematical legacy of ref 1

philosophers in ref 1; see also individual names

Appel, Kenneth ref 1

Archimedes ref 1

Aristotle ref 1

arithmetic:

early ref 1, ref 2

fundamental theorem of ref 1

modular ref 1

symbols and operators for ref 1

see also mathematics; number systems

Arithmetica (Diophantus) ref 1, ref 2

Artificial Intelligence ref 1

astronomy and astrology ref 1, ref 2, ref 3

Australian Aboriginals ref 1

Avogadro’s constant ref 1

Babbage, Charles ref 1

Bede, Venerable ref 1

Berlin Papyrus ref 1

Bernoulli, Daniel ref 1

Bernoulli, Jacob ref 1, ref 2

Bernoulli, Johann ref 1

Bertrand, Joseph ref 1

binary numbers ref 1, ref 2

binomial coefficients ref 1

binomial theorem ref 1

Birthday problem ref 1, ref 2

Blanusa, Danilo ref 1

Bletchley Park ref 1

Bombe ref 1

Book of Addition and Subtraction According to the Hindu Calculation (Al-Khwarizmi) ref 1

Boole, George ref 1

Brahmagupta ref 1

calculator ref 1, ref 2, ref 3, ref 4, ref 5, ref 6

Leibniz’s ref 1

Pascal’s ref 1

calculus ref 1

Fundamental Theorem of ref 1

calendars:

in Dark Ages ref 1

Gregorian ref 1

Julian ref 1, ref 2

Mayans ref 1

Cantor, Georg ref 1

Cardano, Gerolamo ref 1

Cartesian graphs ref 1

catenary curve ref 1

Chaos Game ref 1

chaos theory ref 1

and weather ref 1

Chaucer, Geoffrey ref 1

China ref 1, ref 2

Compendious Book on Calculation . . ., The (Al-Khwarizmi) ref 1

complex numbers ref 1

compound interest ref 1

computers:

and Babbage ref 1

and chaos ref 1

and four-colour theorem ref 1

and fractals ref 1

and Turing ref 1

conic sections ref 1

continuum hypothesis ref 1

coordinates ref 1

Copernicus, Nicolaus ref 1

cosine ref 1

counting:

bone markings for ref 1

on fingers ref 1, ref 2

sheep ref 1

see also mathematics

cryptography ref 1

and frequency analysis ref 1

cubic equations ref 1

cyclic quadrilateral ref 1

De sectionibus conicis (Wallis) ref 1

decimal point ref 1

decimal system ref 1, ref 2, ref 3

deficient numbers ref 1

Descartes, René ref 1, ref 2

Description of the Wonderful Rule of Logarithms (Napier) ref 1

Difference Engine ref 1

difference of two squares ref 1, ref 2

differential equations ref 1, ref 2

differentiation ref 1

Diophantus ref 1, ref 2

‘Epitaph’ of ref 1

distributed computing ref 1

Drake, Frank ref 1

Dresden Codex ref 1, ref 2

economy, beginnings of ref 1

Einstein, Albert ref 1

Elements (Euclid) ref 1, ref 2

Enigma ref 1

see also cryptography

equations ref 1, ref 2, ref 3, ref 4, ref 5, ref 6

and Cartesian graphs ref 1

cubic ref 1

differential ref 1, ref 2

Euler’s identity ref 1

linear ref 1

quadratic ref 1

Eratosthenes ref 1

sieve of ref 1, ref 2

Euclid ref 1, ref 2, ref 3

fifth postulate of ref 1

Euler, Leonhard ref 1, ref 2

and Königsberg bridges ref 1, ref 2

Europe, Middle Ages ref 1

exhaustion, method of ref 1

Exiguus, Dionysius ref 1

extraterrestrial intelligence ref 1

Fermat, Pierre de ref 1, ref 2

Feynman, Richard ref 1

Fibonacci ref 1

fluid mechanics ref 1

four-colour theorem ref 1

fractals ref 1

ultimate ref 1

fractions ref 1, ref 2, ref 3, ref 4

frequency analysis ref 1

Galileo ref 1

Gauss, Carl ref 1

geometry ref 1, ref 2, ref 3

and algebra ref 1

and Euclid ref 1

and pyramids ref 1, ref 2

Goldbach, Christian ref 1

Goldbach conjecture ref 1, ref 2

golden mean ref 1, ref 2

Google/Googol ref 1

gradients ref 1

graph theory ref 1

Guthrie, Francis ref 1

Haken, Wolfgang ref 1

Hall, Monty ref 1

Hardy, Godfrey ref 1

Hawking, Stephen ref 1

Hero ref 1

hexagrams ref 1

hieroglyphics and hieratic writing ref 1

Hilbert, David ref 1, ref 2

Hippasus ref 1

hunter-gatherers ref 1

Huygens, Christiaan ref 1, ref 2

Hypatia ref 1

I Ching ref 1

imaginary numbers ref 1, ref 2

India ref 1

infinity ref 1, ref 2, ref 3

integration ref 1

irrational numbers ref 1

Ishango bone ref 1

Islam ref 1

iteration ref 1, ref 2

Jevons, William ref 1

Jia Xian ref 1

Kanada, Yasumasa ref 1

Kasner, Edward ref 1

Kerckhoff, Auguste ref 1

Key to Mathematics, The (Oughtred) ref 1

Khayyám, Omar ref 1

Koch, Helge von ref 1

Königsberg bridges ref 1, ref 2

Lambert, Johann ref 1

Large Hadron Collider ref 1

large numbers ref 1

Leibniz, Gottfried ref 1, ref 2, ref 3, ref 4, ref 5, ref 6

Leonardo da Vinci ref 1

Leonardo of Pisa (Fibonacci) ref 1

Let’s Make a Deal ref 1

logarithms ref 1, ref 2

natural ref 1, ref 2

and slide rule ref 1

Lorenz, Edward ref 1

Lovelace, Ada ref 1

magic squares ref 1

Mandelbrot, Benoit ref 1

Mandelbrot set ref 1

mathematics:

Ancient Egyptian ref 1, ref 2, ref 3

Ancient Greek ref 1

beginnings of ref 1

in Bronze Age, see Ancient Egypt; Ancient Greeks; Mayans; Mesopotamia

Chinese ref 1

in digital age ref 1

in early civilized era ref 1

future of ref 1

Indian ref 1

Islamic ref 1

language of the universe ref 1

Mayan ref 1

in Mesopotamia ref 1, ref 2, ref 3

in Middle Ages Europe ref 1

modern ref 1

to prove theories ref 1

in Renaissance and after ref 1

Roman ref 1

in Stone Age ref 1

of turbulence ref 1

see also counting

Mayans ref 1, ref 2

calendar of ref 1

and placing of digits ref 1

and Spanish invaders ref 1

Meditations on First Philosophy (Descartes) ref 1

Mesopotamia ref 1, ref 2, ref 3, ref 4

number system of ref 1

Metrodorus ref 1

Millennium problems ref 1

Mises, Richard von ref 1

modular arithmetic ref 1

see also arithmetic

Mohammed ref 1

morphogenesis ref 1

Moscow Mathematical Papyrus ref 1

multiplication ref 1

musical notes and mathematics ref 1

Napier, John ref 1, ref 2

Napier’s bones ref 1

Newton, Isaac ref 1, ref 2, ref 3, ref 4, ref 5, ref 6, ref 7

Nine Chapters on the Mathematical Art ref 1

normal distribution ref 1

number systems:

base-60 (sexagesimal) ref 1

Chinese ref 1

Greek ref 1

Hindu ref 1

Hindu-Arabic ref 1, ref 2, ref 3

Mesopotamian ref 1

and placing of digits ref 1

Ockham’s razor ref 1

operators ref 1

operators and symbols ref 1

Boolean ref 1

Oughtred, William ref 1, ref 2

Pacioli, Luca ref 1

paradoxes ref 1

parallel postulate ref 1

Pascal, Blaise ref 1, ref 2, ref 3, ref 4

triangle of ref 1, ref 2

Wager of ref 1

Perelmann, Grigori ref 1

perfect numbers ref 1

pi ref 1

Pirahã people ref 1

Plato ref 1

Platonic solids ref 1, ref 2

Poincaré Conjecture ref 1

polyhedrons ref 1, ref 2

prime number theorem ref 1

prime numbers ref 1, ref 2, ref 3, ref 4

no pattern to ref 1

Principia Mathematica (Newton) ref 1

probability ref 1

density function of ref 1

Pythagoras ref 1

Diophantus’s interest in ref 1

Pythagorean triples ref 1

Qin Jiushao ref 1

quadratic equations ref 1

Rahn, Johann ref 1

Ramanujan, Srinvasa ref 1

Recorde, Robert ref 1

Renaissance and after ref 1

Rhind Papyrus ref 1

Riemann Hypothesis ref 1

Romans ref 1

numerals of ref 1

set theory ref 1

SETI ref 1

Shannon, Claude ref 1

sheep ref 1

Sierpiński, Waclaw ref 1

sine ref 1

slide rule ref 1, ref 2

Socrates ref 1

square roots ref 1

standard deviation ref 1

Sylvester II, Pope ref 1

symbols and operators ref 1

tangent ref 1, ref 2

Tartaglia, Niccolò Fontana ref 1

tetrahedral numbers ref 1

Teutsche Algebra (Rahn) ref 1

Thales ref 1

three-body problem ref 1

triangles:

area of ref 1

equilateral ref 1

and fractals ref 1

imaginary ref 1

Pascal’s ref 1, ref 2

similar ref 1

triangular numbers ref 1

trigonometry ref 1

trigrams ref 1

triples ref 1

turbulence, mathematics of ref 1

Turing, Alan ref 1, ref 2, ref 3

Turing test ref 1

turning points ref 1

Venn, John ref 1

Vitruvian Man ref 1

Wallis, John ref 1

weather ref 1

weird numbers ref 1

Yang Hui ref 1

Zeno ref 1

zero ref 1, ref 2, ref 3

Zu Chongzhi ref 1