A SCRAP-BOOK OF ELEMENTARY MATHEMATICS
Start Here 1 Alien Encounter 4 Tap-an-Animal 5 Curious Calculations 6 Triangle of Cards 6 Pop-up Dodecahedron 7 Sliced Fingers 8 Turnip for the Books 9 The Four-Colour Theorem 10 Shaggy Dog Story 16 Shaggy Cat Story 18 Rabbits in the Hat 18 River Crossing 1 · Farm Produce 20 More Curious Calculations 20 Extracting the Cherry 22 Make Me a Pentagon 23 What is ·? 23 Legislating the Value of · 24 If They Had Passed It · 25 Empty glasses 26 How Many· 27 Three Quickies 27 Knight's Tours 28 Much Undo About Knotting 29 White-Tailed Cats 31 To Find Fake Coin 32 Perpetual Calendar 35 Mathematical Jokes 1 35 Deceptive Dice 36 An Age-Old Old-Age Problem 37 Why Does Minus Times Minus Make Plus? 37 Heron Suit 38 How to Unmake a Greek Cross 39 How to Remember a Round Number 39 The Bridges of Königsberg 41 How to do Lots of Mathematics 43 Euler's Pentagonal Holiday 44 Ouroborean Rings 44 The Ourotorus 45 Who Was Pythagoras? 46 Proofs of Pythagoras 47 A Constant Bore 49 Fermat's Last Theorem 50 Pythagorean Triples 58 Prime Factoids 59 A Little-Known Pythagorean Curiosity 61 Digital Century 62 Squaring the Square 62 Magic Squares 64 Squares of Squares 66 Ring a-Ring a-Ringroad 67 Pure v Applied 68 Magic Hexagon 68 Pentalpha 69 Wallpaper Patterns 70 How Old Was Diophantus? 71 If You Thought Mathematicians Were Good at Arithmetic · 72 The Sphinx is a Reptile 72 Six Degrees of Separation 73 Trisectors Beware! 76 Langford's Cubes 78 Duplicating the Cube 79 Magic Stars 80 Curves of Constant Width 81 Connecting Cables 81 Coin Swap 82 The Stolen Car 82 Space-Filling Curves 83 Compensating Errors 84 The Square Wheel 84 Why Can't I Divide by Zero? 85 River Crossing 2 · Marital Mistrust 86 Wherefore Art Thou Borromeo? 87 Percentage Play 88 Kinds of People 89 The Sausage Conjecture 89 Tom Fool's Knot 90 New Merology 92 Numerical Spell 94 Spelling Mistakes 95 Expanding Universe 95 What is the Golden Number? 96 What are the Fibonacci Numbers? 98 The Plastic Number 103 Family Occasion 105 Don't Let Go! 105 Theorem: All Numbers are Interesting 105 Theorem: All Numbers are Boring 106 The Most Likely Digit 106 Why Call It a Witch? 109 Möbius and His Band 111 Golden Oldie 113 Three More Quickies 113 Miles of Tiles 114 Chaos Theory 117 Après-Le-Ski 124 Pick's Theorem 125 Mathematical Prizes 126 Why No Nobel for Maths? 128 Is There a Perfect Cuboid? 129 Paradox Lost 130 When Will My MP3 Player Repeat? 131 Six Pens 134 Patented Primes 135 The Poincaré Conjecture 136 Hippopotamian Logic 140 Langton's Ant 141 Pig on a Rope 143 The Surprise Examination 144 Antigravity Cone 144 Mathematical Jokes 2 145 Why Gauss Became a Mathematician 146 What Shape is a Crescent Moon? 150 Famous Mathematicians 150 What is a Mersenne Prime? 151 The Goldbach Conjecture 154 Turtles All the Way Down 155 Hilbert's Hotel 157 Continuum Coaches 160 A Puzzling Dissection 161 A Really Puzzling Dissection 163 Nothing Up My Sleeve · 166 Nothing Down My Leg · 167 Two Perpendiculars 167 Can You Hear the Shape of a Drum? 168 What is e, and Why? 172 May Husband and Ay · 173 Many Knees, Many Seats 174 Euler's Formula 177 What Day is It? 179 Strictly Logical 180 Logical or Not? 180 A Question of Breeding 180 Fair Shares 181 The Sixth Deadly Sin 182 Weird Arithmetic 182 How Deep is the Well? 183 Mc Mahon's Squares 183 What is the Square Root of Minus One? 184 The Most Beautiful Formula 186 Why is Euler's Beautiful Formula True? 186 Your Call May be Monitored for Training Purposes 188 Archimedes, You Old Fraud! 188 Fractals · The Geometry of Nature 189 The Missing Symbol 196 Where There's a Wall, There's a Way 196 Constants to 50 Places 197 Richard's Paradox 197 Connecting Utilities 199 Are Hard Problems Easy? or How to Win a Million Dollars by Proving the Obvious 199 Don't Get the Goat 202 All Triangles are Isosceles 203 Square Year 204 Gödel's Theorems 205 If · isn't a Fraction, How Can You Calculate It? 208 Infinite Wealth 211 Let Fate Decide 212 How Many· 212 What Shape is a Rainbow? 214 Alien Abduction 214 The Riemann Hypothesis 215 Anti-Atheism 220 Disproof of the Riemann Hypothesis 221 Murder in the Park 221 The Cube of Cheese 222 The Game of Life 223 Two-Horse Race 228 Drawing an Ellipse · and More? 230 Mathematical Jokes 3 231 The Kepler Problem 231 The Milk Crate Problem 235 Equal Rights 236 Road Network 236 Tautoverbs 237 Complexity Science 239 Scrabble Oddity 244 Dragon Curve 244 Counterflip 245 Spherical Sliced Bread 246 Mathematical Theology 246 Professor Stewart's Cunning Crib Sheet 251