Reuben Hoar Library (Littleton)

The math book, contributors, Karl Warsi (consultant editor), Jan Dangerfield, Heather Davis, John Farndon, Jonny Griffiths, Tom Jackson, Mukul Patel, Sue Pope, Matt Parker (foreword)

eng

illustrations

index present

non fiction

The math book

1113866167

contributors, Karl Warsi (consultant editor), Jan Dangerfield, Heather Davis, John Farndon, Jonny Griffiths, Tom Jackson, Mukul Patel, Sue Pope, Matt Parker (foreword)

Big ideas simply explained

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

Ancient and classical periods, 6000 BCE-500 CE ; Numerals take their place: 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 algebraThe 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 numbers 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 rood, 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