The Math Book: Big Ideas Simply Explained

Description

See how math's infinite mysteries and beauty unfold in this captivating educational book! Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised with this beautifully illustrated book. Get to know the great minds whose revolutionary discoveries changed our world today. You don't have to be a math genius to follow along with this book! This brilliant book is packed with short, easy-to-grasp explanations, step-by-step diagrams, and witty illustrations that play with our ideas about numbers. What is an imaginary number? Can two parallel lines ever meet? How can math help us predict the future? All will be revealed and explained in this encyclopedia of mathematics. It's as easy as 1-2-3! The Math Book tells the exciting story of how mathematical thought advanced through history. This diverse and inclusive account will have something for everybody, including the math behind world economies and espionage. This book charts the development of math around the world, from ancient mathematical ideas and inventions like prehistoric tally bones through developments in medieval and Renaissance Europe. Fast forward to today and gain insight into the recent rise of game and group theory. Delve in deeper into the history of math: - Ancient and Classical Periods 6000 BCE - 500 CE - The Middle Ages 500 - 1500 - The Renaissance 1500 - 1680 - The Enlightenment 1680 - 1800 - The 19th Century 1800 - 1900 - Modern Mathematics 1900 - Present The Series Simply Explained With over 7 million copies sold worldwide to date, The Math Book is part of the award-winning Big Ideas Simply Explained series from DK Books. It uses innovative graphics along with engaging writing to make complex subjects easier to understand. HOW TO USE THIS EBOOK INTRODUCTION ANCIENT AND CLASSICAL PERIODS 6000 BCE–500 CE Numerals take their places • Positional numbers The square as the highest power • Quadratic equations The accurate reckoning for inquiring into all things • The Rhind papyrus The sum is the same in every direction • Magic squares Number is the cause of gods and daemons • Pythagoras A real number that is not rational • Irrational numbers The quickest runner can never overtake the slowest • Zeno’s paradoxes of motion Their combinations give rise to endless complexities • The Platonic solids Demonstrative knowledge must rest on necessary basic truths • Syllogistic logic The whole is greater than the part • Euclid’s Elements Counting without numbers • The abacus Exploring pi is like exploring the Universe • Calculating pi We separate the numbers as if by some sieve • Eratosthenes’ sieve A geometrical tour de force • Conic sections The art of measuring triangles • Trigonometry Numbers can be less than nothing • Negative numbers The very flower of arithmetic • Diophantine equations An incomparable star in the firmament of wisdom • Hypatia The closest approximation of pi for a millennium • Zu Chongzhi THE MIDDLE AGES 500–1500 A fortune subtracted from zero is a debt • Zero Algebra is a scientific art • Algebra Freeing algebra from the constraints of geometry • The binomial theorem Fourteen forms with all their branches and cases • Cubic equations The ubiquitous music of the spheres • The Fibonacci sequence The power of doubling • Wheat on a chessboard THE RENAISSANCE 1500–1680 The geometry of art and life • The golden ratio Like a large diamond • Mersenne primes Sailing on a rhumb • Rhumb lines A pair of equal-length lines • The equals sign and other symbology Plus of minus times plus of minus makes minus • Imaginary and complex numbers The art of tenths • Decimals Transforming multiplication into addition • Logarithms Nature uses as little as possible of anything • The problem of maxima The fly on the ceiling • Coordinates A device of marvellous invention • The area under a cycloid Three dimensions made by two • Projective geometry Symmetry is what we see at a glance • Pascal’s triangle Chance is bridled and governed by law • Probability The sum of the distance equals the altitude • Viviani’s triangle theorem The swing of a pendulum • Huygens’s tautochrone curve With calculus I can predict the future • Calculus The perfection of the science of numbers • Binary numbers THE ENLIGHTENMENT 1680–1800 To every action there is an equal and opposite reaction • Newton’s laws of motion Empirical and expected results are the same • The law of large numbers One of those strange numbers that are creatures of their own • Euler’s number Random variation makes a pattern • Normal distribution The seven bridges of Königsberg • Graph theory Every even integer is the sum of two primes • The Goldbach conjecture The most beautiful equation • Euler’s identity No theory is perfect • Bayes’ theorem Simply a question of algebra • The algebraic resolution of equations Let us gather facts • Buffon’s needle experiment Algebra often gives more than is asked of her • The fundamental theorem of algebra THE 19TH CENTURY 1800–1900 Complex numbers are coordinates on a plane • The complex plane Nature is the most fertile source of mathematical discoveries • Fourier analysis The imp that knows the positions of every particle in the Universe • Laplace’s demon What are the chances? • The Poisson distribution An indispensable tool in applied mathematics • Bessel functions It will guide the future course of science • The mechanical computer A new kind of function • Elliptic functions I have created another world out of nothing • Non-Euclidean geometries Algebraic structures have symmetries • Group theory Just like a pocket map • Quaternions Powers of natural numbers are almost never consecutive • Catalan’s conjecture The matrix is everywhere • Matrices An investigation into the laws of thought • Boolean algebra A shape with just one side • The Möbius strip The music of the primes • The Riemann hypothesis Some infinities are bigger than others • Transfinite numbers A diagrammatic representation of reasonings • Venn diagrams The tower will fall and the world will end • The Tower of Hanoi Size and shape do not matter, only connections • Topology Lost in that silent, measured space • The prime number theorem MODERN MATHEMATICS 1900–PRESENT The veil behind which the future lies hidden • 23 problems for the 20th century Statistics is the grammar of science • The birth of modern statistics A freer logic emancipates us • The logic of mathematics The Universe is four-dimensional • Minkowski space Rather a dull number • Taxicab numbers A million monkeys banging on a million typewriters • The infinite monkey theorem She changed the face of algebra • Emmy Noether and abstract algebra Structures are the weapons of the mathematician • The Bourbaki group A single machine to compute any computable sequence • The Turing machine Small things are more numerous than large things • Benford’s law A blueprint for the digital age • Information theory We are all just six steps away from each other • Six degrees of separation A small positive vibration can change the entire cosmos • The butterfly effect Logically things can only partly be true • Fuzzy logic A grand unifying theory of mathematics • The Langlands Program Another roof, another proof • Social mathematics Pentagons are just nice to look at • The Penrose tile Endless variety and unlimited complication • Fractals Four colours but no more • The four-colour theorem Securing data with a one-way calculation • Cryptography Jewels strung on an as-yet invisible thread • Finite simple groups A truly marvellous proof • Proving Fermat’s last theorem No other recognition is needed • Proving the Poincaré conjecture DIRECTORY GLOSSARY CONTRIBUTORS QUOTATIONS ACKNOWLEDGEMENTS COPYRIGHT