MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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230 Index MacMahon, Percy Alexander 113, 171, 186 MacMahon’s Color Triangles 113, 115- 116 MacTutor History of Mathematics vi magic v, 16 constant 16 hexagram 16 number 16 star 16 major third 25 major triad 25 Makhuwa 8 Malfatti circles 66 Malfatti, Gian Francesco 65, 162, 184 Malfatti resolvent 162 Malfatti’s Problem 65-66, 162, 166 Maltese cross 20 Manchester University 177 mandorla 22 Manfredi, Gabriele 162 mantra 5 mappings preserving equilateral triangles 75 marble problem 65 Marischal College (Aberdeen) 168 Mars 155 Marshall, W. 72 Martin Co., Glenn L. 178 Marundheeswarar Temple 5 Masonic Lodges 21 Masonic Royal Arch Jewel 21 Mästlin, Michael 155 Mathemagician 182 mathematical biography v competitions v-vi, 129-147 history v properties v, 29-77 recreations v, 103-128 Mathematical Association of America 11, 162, 169, 182 Mathematical Games 119, 182 Mathematical Olympiad of Moldova 145 Republic of China 142 Mathematical Recreations and Essays 176 Mathematical Snapshots 105 Mathematical Time Exposures 105 matrix representation 91-92 maximum area rectangle 41 Maxwell-Boltzmann kinetic theory of gases 168 Maxwell color triangle 88, 168 Maxwell discs 168 Maxwell distribution 169 Maxwell, James Clerk 167, 185 Maxwell materials 169 Maxwell model (generalized) 169 Maxwell’s demon 169 Maxwell’s equations 168-169 Maxwell’s Theorem 169 McCartin, Brian J. 102 McGovern, W. 15 Mécanique analytique 163 Mechanica 161 medial epicondoyle 82 medial triangle 54 Melissen, J. B. M. 44-45 Mersenne, Marin 156-157, 159 Mesolithic 1-2 METAFONT 180 method of exhaustion 150 indivisibles 157 Méthodes nouvelles de la mécanique céleste 170 Method of Mechanical Theorems 151 Meyer Sound 94 Middle Ages 22, 121, 152 midpoint ellipse 51
Index 231 Milan Cathedral 18-19 Millenium Prize Problems 167 minimum order perfect triangulation 72 Minkowski, Hermann 172, 186 Minkowski plane 75, 173 Minkowski spacetime 172 minor triad 25 Miscellaneous Olympiad Problems 146- 147 Mittag-Leffler, Gösta 173 M-matrices 173 Möbius band 194 Modern Puzzles 181 Monad 9 Monckton, Christopher 125 Morandi, Maurizio 44 Morgenstern, Oskar 90 Morley, Frank 171, 186 Morley’s Theorem v, 35, 171-172 Morley triangle 35 Moslems 20 Most Beautiful Theorems in Mathematics 61 MOTET v-vi moth (triangular) 190 Motzkin, T. 77 Mozartkugel 100 Mozart, Wolfgang Amadeus 21, 100 music v, 25 musical chord 25 harmony 10 triangle 192 Musselman, J. R. 39 Musselman’s Theorem 39 nadis 5 Nambokucho period 8 Napoleon’s Theorem v, 36-37 Napoleon triangle 36, 39 NASA 84 NASA Echo I 80 natural equilateral triangles 97-98 Nazi Party 175 nearly-equilateral dissections 73 Nelson, H. L. 107 neopythagoreans 10 Neumann boundary condition 102 neutron star 84 Neville truss 86 New Mathematical Pastimes 171 Newton form 160 Newton’s identities 160 Newton, Sir Isaac 1, 24, 152, 156, 159-161, 184 Newton’s law of cooling 160 Newton’s Laws 160 Newton’s method 160 nine-point center 19, 46 no equilateral triangles on a chess board 61 nonagon (enneagon) 107 nonattacking rooks 126 non-Euclidean equilateral triangles 74 Nordic Mathematics Competition 144 North American Network 79-80 O’Beirne, T. H. 112 octahedral group 26 octahedron 11, 15, 97-98, 117 Odom, George 25-26, 69, 177 olecranon 82 olympiad problems vi On Finite Sums of Rational Numbers 178 On the hypotheses that lie at the foundations of geometry 167 On the number of primes less than a given magnitude 167 optimal spacing (lunar bases) 111 optimal wrapping 100 Order of the Temple 20
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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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132 Mathematical Competitions Figur
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Chapter 6 Biographical Vignettes In
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150 Biographical Vignettes Forms wh
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152 Biographical Vignettes Apolloni
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154 Biographical Vignettes He disco
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156 Biographical Vignettes He fell
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158 Biographical Vignettes give the
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160 Biographical Vignettes Vignette
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162 Biographical Vignettes Swiss 10
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164 Biographical Vignettes sität B
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166 Biographical Vignettes for Eucl
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168 Biographical Vignettes ellipse
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170 Biographical Vignettes Schwarz
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172 Biographical Vignettes the numb
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174 Biographical Vignettes a conseq
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176 Biographical Vignettes topologi
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178 Biographical Vignettes Vignette
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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 240 and 241: 232 Index oriented triangles 70 ori
Page 242 and 243: 234 Index Riemann Surfaces 51, 167
Page 244 and 245: 236 Index Tartaglian Measuring Puzz
Page 246: 238 Index Weber, Wilhelm 164 Weiers
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