About the Authors |
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Introduction |
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xvii | |
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Chapter 1 All About Numbers and Symbols |
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1 | (1) |
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Unit 1 Some Ancient Number Systems |
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1 | (6) |
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Unit 2 The Origin of Our Numerals |
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7 | (2) |
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Unit 3 The History of Zero |
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9 | (3) |
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Unit 4 The Origin of the Equal Sign |
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12 | (2) |
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Unit 5 The Birth of Multiplication and its Symbol |
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14 | (4) |
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Unit 6 The Origin of the Division Symbols |
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18 | (3) |
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Unit 7 The Origins of Fractions |
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21 | (2) |
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Unit 8 The Emergence of Exponent Notation |
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23 | (2) |
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Unit 9 The Origin of the Square-Root Symbol |
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25 | (2) |
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Unit 10 The Origin of Percent %, Number #, and Dollar $ Symbols |
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27 | (3) |
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Unit 11 The Ubiquitous Number π |
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30 | (4) |
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Unit 12 One of the Earliest Approximations of it |
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34 | (2) |
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Unit 13 The Origin of the Basic Trigonometric Names: Sine, Tangent, and Secant |
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36 | (2) |
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Unit 14 How Numbers are Categorized |
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38 | (2) |
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Unit 15 Imaginary Numbers are Not Really Imaginary |
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40 | (7) |
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Unit 16 The Birth of Algebra |
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47 | (1) |
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Unit 17 The Infinity Concept and Its Symbol ∞ |
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48 | (8) |
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Unit 18 The "Quad" in Quadratic |
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56 | (1) |
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Unit 19 Prime Numbers: Background and Properties |
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57 | (6) |
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63 | (4) |
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Unit 21 Triangular Numbers and Their Relation to Square Numbers |
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67 | (4) |
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71 | (3) |
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Unit 23 Very Small and Very Large Numbers |
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74 | (3) |
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Unit 24 The Googol is Much Older Than Google |
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77 | (2) |
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Unit 25 Armstrong or Narcissistic Numbers |
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79 | (4) |
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Unit 26 Friendly Numbers or Amicable Numbers |
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83 | (4) |
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Unit 27 Happy and Unhappy Numbers |
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87 | (3) |
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Unit 28 Repunits, Numbers Consisting Only of 1's |
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90 | (5) |
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Unit 29 Palindromic Numbers |
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95 | (6) |
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Unit 30 The Ubiquitous Number 1089 |
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101 | (2) |
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103 | (4) |
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Unit 32 The Transcendency of Transcendental Numbers |
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107 | (2) |
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Chapter 2 Arithmetic Curiosities |
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109 | (52) |
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Unit 33 How the Romans did Multiplication |
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109 | (4) |
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Unit 34 How Complex Calculations Were Done Before Electronics |
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113 | (7) |
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Unit 35 American and European Subtraction Algorithms |
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120 | (2) |
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Unit 36 Extracting a Square Root |
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122 | (1) |
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Unit 37 Divisibility by Prime Numbers |
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123 | (6) |
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Unit 38 Successive Percentages |
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129 | (2) |
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Unit 39 Casting Out Nines |
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131 | (4) |
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135 | (1) |
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Unit 41 Mistaken Assumptions |
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136 | (3) |
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Unit 42 The Ulam-Collatz Loop |
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139 | (2) |
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Unit 43 A Cyclic Number Loop |
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141 | (3) |
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Unit 44 Curious Number Properties |
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144 | (10) |
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154 | (7) |
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Chapter 3 Aspects of Measurement |
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161 | (34) |
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Unit 46 The Origin of Measurement |
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161 | (3) |
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Unit 47 The Metric System Versus the U.S. Customary System |
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164 | (4) |
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Unit 48 The Origins of Today's Calendar |
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168 | (5) |
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Unit 49 How Eratosthenes Measured the Earth |
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173 | (2) |
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Unit 50 The Origin of the Cartesian Plane |
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175 | (5) |
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Unit 51 Why the Normal Bell-Shaped Curve is Called Normal |
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180 | (3) |
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Unit 52 Measures of Central Tendency |
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183 | (3) |
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Unit 53 Comparing Means Algebraically |
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186 | (2) |
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Unit 54 Comparing the Three Means Geometrically |
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188 | (3) |
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191 | (4) |
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Chapter 4 Geometric Novelties |
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195 | (90) |
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Unit 56 The Platonic Solids |
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195 | (2) |
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Unit 57 Euler's Theorem Revisited |
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197 | (4) |
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Unit 58 The Beginnings of Geometry |
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201 | (5) |
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Unit 59 The Origin of the American Secondary School Geometry Course |
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206 | (3) |
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Unit 60 The Pythagorean Theorem and Its Origins |
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209 | (11) |
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Unit 61 President James A. Garfield's Contribution to Mathematics |
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220 | (3) |
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Unit 62 The Golden Ratio -- and the Golden Rectangle and Triangle |
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223 | (6) |
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Unit 63 The Center of Gravity of Triangles and Quadrilaterals |
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229 | (3) |
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Unit 64 Napoleon's Geometry Theorem |
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232 | (6) |
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238 | (1) |
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Unit 66 The Nine-Point Circle |
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239 | (5) |
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Unit 67 A Famous Problem of Antiquity -- Angle Trisection |
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244 | (4) |
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Unit 68 The Ever-Present Equilateral Triangle |
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248 | (4) |
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Unit 69 The Four-Color Map Problem |
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252 | (3) |
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Unit 70 Optical Illusions |
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255 | (4) |
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Unit 71 The World of Non-Euclidean Geometries |
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259 | (5) |
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Unit 72 Introduction to Spherical Geometry |
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264 | (11) |
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Unit 73 Cartography is Mathematically Challenging |
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275 | (3) |
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Unit 74 A Look at Fractals |
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278 | (7) |
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285 | (24) |
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Unit 75 The History of Probability |
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285 | (2) |
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Unit 76 The Famous Birthday Problem |
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287 | (2) |
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Unit 77 The Remarkable Probability in the Game of Craps |
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289 | (4) |
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Unit 78 Some Statements are Neither True nor False |
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293 | (2) |
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Unit 79 The Pigeonhole Principle |
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295 | (1) |
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Unit 80 The Heads and Tails Conundrum |
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296 | (1) |
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Unit 81 The Monty Hall Problem |
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297 | (3) |
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Unit 82 The False Positive Paradox |
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300 | (3) |
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303 | (6) |
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Chapter 6 A Potpourri of Mathematical Topics |
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309 | (66) |
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309 | (1) |
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Unit 85 More Mathematical Conundrums |
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310 | (2) |
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Unit 86 Mistakes in Mathematics |
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312 | (9) |
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Unit 87 The Hands of an Analog Clock |
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321 | (3) |
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Unit 88 Pythagorean Triples |
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324 | (3) |
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Unit 89 Fermat's Last Theorem |
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327 | (3) |
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Unit 90 Pure Mathematics and Prime Numbers |
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330 | (3) |
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Unit 91 The Fibonacci Numbers |
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333 | (7) |
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Unit 92 Diophantine Equations |
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340 | (3) |
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Unit 93 The Goldbach Conjecture |
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343 | (2) |
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Unit 94 Triskaidekaphobia |
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345 | (5) |
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Unit 95 The Parabola -- A Very Special Curve |
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350 | (5) |
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Unit 96 Kepler's Three Famous Laws |
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355 | (3) |
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Unit 97 Beyond the Quadratic Equation |
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358 | (3) |
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Unit 98 Evariste Galois -- A Short Brilliant Life |
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361 | (3) |
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Unit 99 A Look at Einstein's Special Relativity |
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364 | (2) |
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Unit 100 A Clear Look at Calculus |
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366 | (4) |
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Unit 101 Euler's Remarkable Relationship |
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370 | (5) |
Index |
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375 | |