DK-Mathematics-ajk$15.99# 1,8158,815,nof,eng,20210323,20210401,5,DK:The Maths Book: Big Ideas Simply Explained Kindle Edition ama,https://www.amazon.com/Maths-Book-Ideas-Simply-Explained-ebook/dp/B07TNF2LPY/ref=tmm_kin_swatch_0?_encoding=UTF8&qid=1616486056&sr=8-2 eng, bones through to the developments in mathematics during 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 maths: - Ancient and Classical Periods 6000 BCE - 500 CE - The Middle Ages 500 - 1500 - The Renaissance 1500 - 1680 - The Enlightenment 1680 - 1800 - The 19 th Century 1800 - 1900 - Modern Mathematics 1900 - Present The Series Simply Explained With over 7 million copies sold worldwide to date, The Maths Book is part of the award-winning Big Ideas series from DK Books. It uses innovative graphics 13,c,CONTENTS HOW TO USE THIS EBOOK 17,2,INTRODUCTION 17,h,They also demonstrate that the history of mathematics is above all a story of discovery rather than invention. 18,h,When mathematicians first showed that the angles of any triangle in a flat plane when added together come to 180°, a straight line, this was not their invention: they had simply discovered a fact that had always been (and will always be) true. 19,w,ziggurat /ˈziɡəˌrat/ I. noun (in ancient Mesopotamia) a rectangular stepped tower, sometimes surmounted by a temple. Ziggurats are first attested in the late 3rd millennium BC and probably inspired the biblical story of the Tower of Babel (Gen. 11:1–9). – origin from Akkadian ziqqurratu. 20,h,It is impossible to be a mathematician without being a poet of the soul. Sofya Kovalevskaya Russian mathematician 21,3,Arithmetic and algebra 25,q,In mathematics, the art of asking questions is more valuable than solving problems. Georg Cantor German mathematician 27,q,Mathematics, rightly viewed, possesses not only truth, but supreme beauty. Bertrand Russell British philosopher and mathematician 28,1 ANCIENT AND CLASSICAL PERIODS 6000 BCE–500 CE 29,h,the Egyptians had used a triangle with sides of 3, 4, and 5 units as a building tool to ensure corners were square. 30,b,20210323 +30=30 4% DK The Maths Book (Big Ideas) epa 31,2,Numerals take their places • Positional numbers 32,q,It is given to us to calculate, to weigh, to measure, to observe; this is natural philosophy. Voltaire French philosopher 34,h,such as 22, indicates (2 × 10upcase1) + 2; the value of the 2 on the left is ten times that of the 2 on the right. Placing digits after the number 22 will create hundreds, thousands, and larger powers of 10. 351w wedge /wej/ I. noun 1. a piece of wood, metal, or some other material having one thick end and tapering to a thin edge, that is driven between two objects or parts of an object to secure or separate them. 2. an object or piece of something having the shape of a wedge • a wedge of cheese. 3. a formation of people or animals in the shape of a wedge. 4. a golf club with a low, angled face for maximum loft. 43,2,The square as the highest power • Quadratic equations 50,q,Politics is for the present, but an equation is for eternity. Albert Einstein 54,2,The accurate reckoning for inquiring into all things • The Rhind papyrus 55,h,c. 1800 BCE The Moscow papyrus provides solutions to 25 mathematical problems, including the calculation of the surface area of a hemisphere and the volume of a pyramid. 62,2,The sum is the same in every direction • Magic squares 67,2,Number is the cause of gods and daemons • Pythagoras 70,h,The smallest, or most primitive, of the Pythagorean triples is a triangle with side lengths 3, 4, and 5. As this graphic shows, 9 plus 16 equals 25. 72,h,The Egyptians knew that a triangle with sides of 3, 4, and 5 (the first Pythagorean triple) would produce a right angle, so their surveyors used ropes of these lengths to construct perfect right angles for their building projects. 73,q,Reason is immortal, all else is mortal. Pythagoras 75,h,The first perfect number is 6, as its divisors 1, 2, and 3 add up to 6. The second is 28 (1 + 2 + 4 + 7 + 14 = 28), the third 496, and the fourth 8,128. 76,b,20210324 +46=76 10% DK The Maths Book (Big Ideas) epa 77,3,An integrated philosophy 83,2,A real number that is not rational • Irrational numbers 88,2,The quickest runner can never overtake the slowest • Zeno’s paradoxes of motion 92,2,Their combinations give rise to endless complexities • The Platonic solids 97,2,Demonstrative knowledge must rest on necessary basic truths • Syllogistic logic 102,2,The whole is greater than the part • Euclid’s Elements 112,q,Geometry is knowledge of what always exists. Plato 117,2,Counting without numbers • The abacus 118,h,c. 3000 BCE South American Indians record numbers by tying knots in string. c. 2000 BCE The Babylonians develop positional numbers. AFTER 1202 Leonardo of Pisa (Fibonacci) commends the Hindu–Arabic number system in Liber Abaci. 1621 In England, William Oughtred invents the slide rule, which simplifies the use of logarithms. 1972 Hewlett Packard invents an electronic scientific calculator for personal use. 120,h,The suanpan shown here is set to the number 917,470,346. The suanpan is traditionally a 2:5 abacus – each column has two “heaven” beads, each with a value of 5, and 5 “earth” beads, each with a value of 1, giving a potential value of 15 units. This allows for calculations involving the Chinese base-16 system, which uses 15 units rather than the 9 used in the decimal system. 123,2,Exploring pi is like exploring the Universe • Calculating pi 137,2,We separate the numbers as if by some sieve • Eratosthenes’ sieve 142,2,A geometrical tour de force • Conic sections 147,2,The art of measuring triangles • Trigonometry 12 154,q,A logarithmic table is a small table by the use of which we can obtain knowledge of all geometrical dimensions and motions in space. John Napier 159,2,Numbers can be less than nothing • Negative numbers 160,h,Only in the 17th century did European mathematicians begin to fully accept negative numbers. 162,h,In the Chinese rod numeral system, red indicates positive numbers, while black indicates negative numbers. To make the number being represented as clear as possible, horizontal and vertical symbols are used alternately – for example, the number 752 would use a vertical 7, then a horizontal 5, followed by a vertical 2. Blank spaces represent zero. 166,h,Mathematics in ancient China Jiuzhang suanshu, or The Nine Chapters on the Mathematical Art, reveals the mathematical methods known to the ancient Chinese. It is written as a collection of 246 practical problems and their solutions. 167,2,The very flower of arithmetic • Diophantine equations 173,2,An incomparable star in the firmament of wisdom • Hypatia 176,2,The closest approximation of pi for a millennium • Zu Chongzhi 178,h,In the 3rd century, Liu Hui approached the task using the same method as Archimedes – drawing regular polygons with increasing numbers of sides inside and outside a circle. He found that a 96-sided polygon allowed a calculation of π as 3.14, but by repeatedly doubling the number of sides up to 3,072, he reached a value of 3.1416. 179,b,20210324 +103=179 23% DK The Maths Book (Big Ideas) epa 180,2,THE MIDDLE AGES 500–1500 183,2,A fortune subtracted from zero is a debt 191,h,Europeans finally accepted zero in the 17th century, when English mathematician John Wallis incorporated zero in his number line. 193,2,Algebra is a scientific art • Algebra 196,w,The word “algebra” comes from al-jabr. 199,q,The principal object of Algebra… is to determine the value of quantities which were before unknown… by considering attentively the conditions given… expressed in known numbers. Leonhard Euler 208,2,Freeing algebra from the constraints of geometry • The binomial theorem 214,2,Fourteen forms with all their branches and cases • Cubic equations 224,h,The new Jalali calendar, named after the sultan, was adopted on 15 March 1079 and was only modified in 1925. 224,2,The ubiquitous music of the spheres • The Fibonacci sequence 233,h,Although it is often associated with the arts, the Fibonacci sequence has also proved a useful tool in finance. Today, ratios derived from the sequence are used as an analytical tool to forecast the point at which stock market prices will stop rising or falling. 233,h,A piano keyboard scale from C to C spans 13 keys, eight white and five black. The black keys are in groups of two and three. These numbers all form part of the Fibonacci sequence. 235,2,The power of doubling • Wheat on a chessboard 239,b,20210325 +60=239 30% DK The Maths Book (Big Ideas) epa 240,1,THE RENAISSANCE 1500–1680 243,2,The geometry of art and life • The golden ratio 243,h,For Newton, calculus was a practical tool for his work in physics and especially on the motion of planets, but Leibniz recognized its theoretical importance and refined the rules of differentiation and integration. 255,2,For Newton, calculus was a practical tool for his work in physics and especially on the motion of planets, but Leibniz recognized its theoretical importance and refined the rules of differentiation and integration. 255,2,Like a large diamond • Mersenne primes 258,2,Sailing on a rhumb • Rhumb lines 261,2,A pair of equal-length lines • The equals sign and other symbology 266,2,Plus of minus times plus of minus makes minus • Imaginary and complex numbers 276,2,The art of tenths • Decimals 288,2,Transforming multiplication into addition • Logarithms 299,2,Nature uses as little as possible of anything • The problem of maxima 305,2,The fly on the ceiling • Coordinates 322,2,A device of marvellous invention • The area under a cycloid 327,2,Three dimensions made by two • Projective geometry 333,2,Symmetry is what we see at a glance • Pascal’s triangle 344,2,Chance is bridled and governed by law • Probability 354,2,The sum of the distance equals the altitude • Viviani’s triangle theorem 358,2,The swing of a pendulum • Huygens’s tautochrone curve 360,2,With calculus I can predict the future • Calculus 377,2,The perfection of the science of numbers • Binary numbers 383,2,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 811,b,20210401 +46=76 10% DK The Maths Book (Big Ideas) epa ###enrufi @@@ *** K. The Maths Book (Big Ideas) . Dorling Kindersley Ltd. Kindle Edition.