MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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182 Biographical Vignettes meeting) but broke it off, accusing Loyd of plagiarism. His hobbies, other than puzzling, included billiards, bowling and, especially, croquet, and he was a skilled pianist and organist. A selection of his puzzles are considered in Recreations 2-5 of Chapter 4. He died at his home in Lewes, Sussex, aged 73. Vignette 45 (Martin Gardner: 1914-2010). For 25 years Martin Gardner wrote “Mathematical Games and Recreations”, a monthly column for Scientific American magazine. (An anthology of these columns is available in [137].) He was the author of more than 70 books, the vast majority of which deal with mathematical topics. He was born and grew up in Tulsa, Oklahoma. He earned a degree in philosophy from University of Chicago and also began graduate studies there. He served in the U.S. Navy during World War II as ship’s secretary aboard the destroyer escort USS Pope. For many years, he lived in Hastings-on-Hudson, New York (on Euclid Avenue!) and earned his living as a freelance writer, although in the early 1950’s he was editor of Humpty Dumpty Magazine. In 1979, he semiretired and moved to Henderson, North Carolina. In 2002, he returned home to Norman, Oklahoma. Some of his more notable contributions to Recreational Mathematics are discussed in Property 22 of Chapter 2 and Recreation 20 of Chapter 4. Despite not being a “professional” mathematician, the American Mathematical Society awarded him the Steele Prize in 1987, in recognition of the generations of mathematicians inspired by his writings. The Mathematical Association of America has honored him for his contributions by holding a special session on Mathematics related to his work at its annual meeting in 1982 and by making him an Honorary Member of the Association. He was also an amateur magician thereby making him a bona fide Mathemagician! He died at a retirement home in Norman, aged 95.
Biographical Vignettes 183 Figure 6.2: Pythagoras Figure 6.3: Plato Figure 6.4: Euclid Figure 6.5: Archimedes Figure 6.6: Apollonius Figure 6.7: Pappus Figure 6.8: Fibonacci Figure 6.9: Da Vinci Figure 6.10: Tartaglia
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MYSTERIES OF THE EQUILATERAL TRIANG
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Dedicated to our beloved Beta Katze
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Preface v PREFACE Welcome to Myster
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Contents Preface . . . . . . . . .
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2 History Lepenski Vir, located on
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4 History counter the sister-states
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6 History Figure 1.11: Chinese Wind
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8 History Wasan which was usually s
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10 History Figure 1.17: Pythagorean
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12 History Figure 1.24: Five Platon
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14 History Figure 1.26: Eight Conve
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16 History (a) (b) (c) Figure 1.31:
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18 History The equilateral triangle
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20 History Figure 1.36: Gothic Maso
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22 History Figure 1.40: Vesica Pisc
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24 History Figure 1.43: Alchemical
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26 History Modern sculpture has not
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28 History (a) (b) Figure 1.49: Tri
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30 Mathematical Properties The rela
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32 Mathematical Properties Figure 2
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38 Mathematical Properties 2.14(b)
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40 Mathematical Properties - Combin
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44 Mathematical Properties be the s
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56 Mathematical Properties (a) (b)
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58 Mathematical Properties Property
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72 Mathematical Properties The best
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74 Mathematical Properties in colum
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Chapter 3 Applications of the Equil
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80 Applications Application 2 (Sate
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82 Applications The ei are the proj
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84 Applications (a) Figure 3.9: (a)
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86 Applications Figure 3.11: Warren
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88 Applications Figure 3.14: Maxwel
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90 Applications Figure 3.17: De Fin
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92 Applications (a) (b) Figure 3.20
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94 Applications (a) Figure 3.23: Lo
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96 Applications Application 25 (Squ
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98 Applications (a) Figure 3.28: Na
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100 Applications (a) (b) (c) (d) Fi
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102 Applications The eigenstructure
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104 Mathematical Recreations Figure
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108 Mathematical Recreations (a) (b
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112 Mathematical Recreations of pla
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120 Mathematical Recreations and n
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124 Mathematical Recreations (a) Fi
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128 Mathematical Recreations Recrea
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130 Mathematical Competitions Probl
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Page 188 and 189: 180 Biographical Vignettes and Recr
Page 192 and 193: 184 Biographical Vignettes Figure 6
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Page 196 and 197: Appendix A Gallery of Equilateral T
Page 198 and 199: 190 Gallery Figure A.8: ET Wing Fig
Page 200 and 201: 192 Gallery Figure A.18: ET Bowling
Page 202 and 203: 194 Gallery Figure A.28: ET Escher
Page 204 and 205: 196 Gallery Figure A.36: ET Street
Page 206 and 207: 198 Gallery Figure A.44: ET Tragedy
Page 208 and 209: 200 Bibliography [12] J. Aubrey, Br
Page 210 and 211: 202 Bibliography [42] R. Calinger,
Page 212 and 213: 204 Bibliography [74] J.-P. Delahay
Page 214 and 215: 206 Bibliography [106] J. A. Flint,
Page 216 and 217: 208 Bibliography [138] M. Gardner,
Page 218 and 219: 210 Bibliography [169] H. Hellman,
Page 220 and 221: 212 Bibliography [199] M. Kraitchik
Page 222 and 223: 214 Bibliography [229] T. H. O’Be
Page 224 and 225: 216 Bibliography [260] B. Russell,
Page 226 and 227: 218 Bibliography [290] S. K. Stein,
Page 228 and 229: 220 Bibliography [319] A. Weil, Num
Page 230 and 231: 222 Index Barbier’s Theorem 56 ba
Page 232 and 233: 224 Index Cruise, Tom 24 Crusades 2
Page 234 and 235: 226 Index ture 157 Fermat’s Princ
Page 236 and 237: 228 Index house (triangular) 197 Hu
Page 238 and 239: 230 Index MacMahon, Percy Alexander
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232 Index oriented triangles 70 ori
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234 Index Riemann Surfaces 51, 167
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236 Index Tartaglian Measuring Puzz
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238 Index Weber, Wilhelm 164 Weiers
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