The math book : [big ideas simply explained

Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised, and the great minds behind them, with this original, graphics-led book. Applying the Big Ideas Simply Explained series' trademark combination of authoritative, accessible text and bold graphics to chart the development of math through history, The Math Book explores and explains subjects ranging from ancient mathematical ideas and inventions, such as prehistoric tally bones and Sumerian multiplication tables, through the developments in mathematics during medieval and Renaissance Europe, to the more recent rise of game and group theory. Tracing math through the scientific revolution to its 21st-century use in computers, the internet, and AI, The Math Book uses an innovative graphic-led approach to make the subject accessible to everyone. 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 marvelous 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 colors but no more • The four-color theorem Securing data with a one-way calculation • Cryptography Jewels strung on an as-yet invisible thread • Finite simple groups A truly marvelous proof • Proving Fermat’s last theorem No other recognition is needed • Proving the Poincaré conjecture DIRECTORY GLOSSARY CONTRIBUTORS QUOTATIONS ACKNOWLEDGMENTS COPYRIGHT Пустая страница Learn about the most important mathematical ideas, theorems, and movements in The Math Book. Part of the fascinating Big Ideas series, this book tackles tricky topics and themes in a simple and easy to follow format. Learn about Math in this overview guide to the subject, brilliant for novices looking to find out more and experts wishing to refresh their knowledge alike! The Math Book brings a fresh and vibrant take on the topic through eye-catching graphics and diagrams to immerse yourself in. This captivating book will broaden your understanding of Math, with: - More than 85 ideas and events key to the development of mathematics - Packed with facts, charts, timelines and graphs to help explain core concepts - A visual approach to big subjects with striking illustrations and graphics throughout - Easy to follow text makes topics accessible for people at any level of understanding The Math Book is a captivating introduction to the world’s most famous theorems, mathematicians and movements, aimed at adults with an interest in the subject and students wanting to gain more of an overview. Charting the development of math around the world from Babylon to Bletchley Park, this book explains how math help us understand everything from patterns in nature to artificial intelligence. Your Math Questions, Simply Explained What is an imaginary number? Can two parallel lines ever meet? How can math help us predict the future? This engaging overview explores answers to big questions like these and how they contribute to our understanding of math. If you thought it was difficult to learn about topics like algebra and statistics, The Math Book presents key information in an easy to follow layout. Learn about the history of math, from ancient ideas such as magic squares and the abacus to modern cryptography, fractals, and the final proof of Fermat’s Last Theorem. The Big Ideas Series With millions of copies sold worldwide, The Math Book is part of the award-winning Big Ideas series from DK. The series uses striking graphics along with engaging writing, making big topics easy to understand. 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. Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised, and the great minds behind them, with this original and colorful book. Take a journey through the fascinating story of fractions, numbers, patterns, and shapes in order to better understand the complex world we live in. Continuing the "Big Ideas" series' trademark combination of authoritative, clear text and bold graphics to chart the development of math through history, the book explores and explains some of the most complex and fascinating mathematical subjects. Delve into everything from the mathematical ideas and inventions of the ancient world such as the first number systems, magic squares, and the Chinese abacus, through to the developments in mathematics during medieval and Renaissance Europe, to the rise of group theory and cryptography more recently. This diverse and inclusive account of mathematics will have something for everybody: for those interested in the maths behind world economies, secret spies, modern technology and plenty more, taking readers around the world from Babylon to Bletchley Park. Tracing maths through the Scientific Revolution to its 21st-century use in computers, the internet, and AI, The Math Book uses an innovative visual approach to make the subject accessible to everyone, casual readers and students alike **Discover more than 85 of the most important mathematical ideas, theorems, and proofs ever devised, and the great minds behind them, with this original, graphics-led book.**__Big Ideas Simply Explained____The Math Book____The Math Book__