MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

More documents

Recommendations

Info

204 Bibliography [74] J.-P. Delahaye, Le Fascinant Nombre π, Belin·Pour La Science, Paris, 1997. [75] E. D. Demaine, M. L. Demaine, J. Iacono and S. Langerman, “Wrapping Spheres with Flat Paper”, Computational Geometry: Theory and Applications, Vol. 42, No. 8 (2009), pp. 748-757. [76] J. Derbyshire, Prime Obsession, Joseph Henry Press, Washington, DC, 2003. [77] R. Descartes, La Géométrie, Dover, New York, NY, 1954. [78] K. Devlin, The Millenium Problems, Basic Books, New York, NY, 2002. [79] W. R. Dickinson and C. A. Suczek, “Plate Tectonics and Sandstone Compositions”, American Association of Petroleum Geologists Bulletin, Vol. 63, No. 12 (December 1979), pp. 2164-2182. [80] E. J. Dijksterhuis, Archimedes, Princeton University Press, Princeton, NJ, 1987. [81] C. W. Dodge, Euclidean Geometry and Transformations, Dover, Mineola, NY, 2004. [82] C. L. Dodgson, Curiosa Mathematica, Part 2: Pillow Problems, Third Edition, Macmillan, London, 1894. [83] E. P. Doolan, “A Sacred Geometry of the Equilateral Triangle”, International Journal of Mathematical Education in Science and Technology, Vol. 39, No. 5 (2008), pp. 601-629. [84] H. Dörrie, 100 Great Problems of Elementary Mathematics: Their History and Solution, Dover, New York, NY, 1965. [85] H. E. Dudeney, The Canterbury Puzzles, Dover, Mineola, NY, 1958. [86] H. E. Dudeney, Amusements in Mathematics, Dover, Mineola, NY, 1958. [87] H. E. Dudeney, 536 Puzzles & Curious Problems, M. Gardner (Editor), Scribner, New York, NY, 1967. [88] C. Dumontier, Clinical Examination of the Elbow, http://www.maitrise-orthop.com/corpusmaitri/orthopaedic/ mo77_dumontier/index_us.shtml. [89] W. Dunham (Editor), The Genius of Euler: Reflections on his Life and Work, Mathematical Association of America, Washington, DC, 2007.
Bibliography 205 [90] G. W. Dunnington, Gauss: Titan of Science, The Mathematical Association of America, Washington, DC, 2004. [91] D. S. Dye, Chinese Lattice Designs, Harvard-Yenching Institute Monograph Series 5-6, Dover, Mineola, NY, 1974. [92] A. W. F. Edwards, Foundations of Mathematical Genetics, Second Edition, Cambridge University Press, Cambridge, 2000. [93] A. W. F. Edwards, Pascal’s Arithmetical Triangle: The Story of a Mathematical Idea, The Johns Hopkins University Press, Baltimore, MD, 2002. [94] H. G. Eggleston, Problems in Euclidean Space: Application of Convexity, Dover, Mineola, NY, 2007. [95] D. Erdély, Spidron System, http://edan.szinhaz.org/SpidroNew/. [96] P. Erdös and J. Surányi, Topics in the Theory of Numbers, Springer, New York, NY, 2003. [97] H. Eves, A Survey of Geometry, Revised Edition, Allyn and Bacon, Boston, MA, 1972. [98] H. Eves, Great Moments in Mathematics (Before 1650), Mathematical Association of America, Washington, DC, 1983. [99] J. D. Faires and D. Wells, The Contest Problem Book VIII (AMC 10): 2000-2007, Mathematical Association of America, Washington, DC, 2008. [100] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Wiley, Chichester, 1990. [101] H. Fantel, “Major de Seversky’s Ion-Propelled Aircraft”, Popular Mechanics, Vol. 122, No. 2 (August 1964), pp. 58-61, p. 194, p. 196. [102] E. A. Fellmann, Leonhard Euler, Birkhäuser, Basel, 2007. [103] Z. Feng, M. M. Wood, and C. Rousseau, USA and International Mathematical Olympiads 2005, Mathematical Association of America, Washington, DC, 2006. [104] Z. Feng, and Y. Zhao, USA and International Mathematical Olympiads 2006-2007, Mathematical Association of America, Washington, DC, 2008. [105] K. Ferguson, Tycho & Kepler, Walker, New York, NY, 2002.
Page 1 and 2:
MYSTERIES OF THE EQUILATERAL TRIANG
Page 3 and 4:
Dedicated to our beloved Beta Katze
Page 5 and 6:
Preface v PREFACE Welcome to Myster
Page 7:
Contents Preface . . . . . . . . .
Page 10 and 11:
2 History Lepenski Vir, located on
Page 12 and 13:
4 History counter the sister-states
Page 14 and 15:
6 History Figure 1.11: Chinese Wind
Page 16 and 17:
8 History Wasan which was usually s
Page 18 and 19:
10 History Figure 1.17: Pythagorean
Page 20 and 21:
12 History Figure 1.24: Five Platon
Page 22 and 23:
14 History Figure 1.26: Eight Conve
Page 24 and 25:
16 History (a) (b) (c) Figure 1.31:
Page 26 and 27:
18 History The equilateral triangle
Page 28 and 29:
20 History Figure 1.36: Gothic Maso
Page 30 and 31:
22 History Figure 1.40: Vesica Pisc
Page 32 and 33:
24 History Figure 1.43: Alchemical
Page 34 and 35:
26 History Modern sculpture has not
Page 36 and 37:
28 History (a) (b) Figure 1.49: Tri
Page 38 and 39:
30 Mathematical Properties The rela
Page 40 and 41:
32 Mathematical Properties Figure 2
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
38 Mathematical Properties 2.14(b)
Page 48 and 49:
40 Mathematical Properties - Combin
Page 50 and 51:
Page 52 and 53:
44 Mathematical Properties be the s
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
56 Mathematical Properties (a) (b)
Page 66 and 67:
58 Mathematical Properties Property
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
72 Mathematical Properties The best
Page 82 and 83:
74 Mathematical Properties in colum
Page 84 and 85:
Page 86 and 87:
Chapter 3 Applications of the Equil
Page 88 and 89:
80 Applications Application 2 (Sate
Page 90 and 91:
82 Applications The ei are the proj
Page 92 and 93:
84 Applications (a) Figure 3.9: (a)
Page 94 and 95:
86 Applications Figure 3.11: Warren
Page 96 and 97:
88 Applications Figure 3.14: Maxwel
Page 98 and 99:
90 Applications Figure 3.17: De Fin
Page 100 and 101:
92 Applications (a) (b) Figure 3.20
Page 102 and 103:
94 Applications (a) Figure 3.23: Lo
Page 104 and 105:
96 Applications Application 25 (Squ
Page 106 and 107:
98 Applications (a) Figure 3.28: Na
Page 108 and 109:
100 Applications (a) (b) (c) (d) Fi
Page 110 and 111:
102 Applications The eigenstructure
Page 112 and 113:
104 Mathematical Recreations Figure
Page 114 and 115:
Page 116 and 117:
108 Mathematical Recreations (a) (b
Page 118 and 119:
Page 120 and 121:
112 Mathematical Recreations of pla
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
120 Mathematical Recreations and n
Page 130 and 131:
Page 132 and 133:
124 Mathematical Recreations (a) Fi
Page 134 and 135:
Page 136 and 137:
128 Mathematical Recreations Recrea
Page 138 and 139:
130 Mathematical Competitions Probl
Page 140 and 141:
132 Mathematical Competitions Figur
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Chapter 6 Biographical Vignettes In
Page 158 and 159:
150 Biographical Vignettes Forms wh
Page 160 and 161:
152 Biographical Vignettes Apolloni
Page 162 and 163: 154 Biographical Vignettes He disco
Page 164 and 165: 156 Biographical Vignettes He fell
Page 166 and 167: 158 Biographical Vignettes give the
Page 168 and 169: 160 Biographical Vignettes Vignette
Page 170 and 171: 162 Biographical Vignettes Swiss 10
Page 172 and 173: 164 Biographical Vignettes sität B
Page 174 and 175: 166 Biographical Vignettes for Eucl
Page 176 and 177: 168 Biographical Vignettes ellipse
Page 178 and 179: 170 Biographical Vignettes Schwarz
Page 180 and 181: 172 Biographical Vignettes the numb
Page 182 and 183: 174 Biographical Vignettes a conseq
Page 184 and 185: 176 Biographical Vignettes topologi
Page 186 and 187: 178 Biographical Vignettes Vignette
Page 188 and 189: 180 Biographical Vignettes and Recr
Page 190 and 191: 182 Biographical Vignettes meeting)
Page 192 and 193: 184 Biographical Vignettes Figure 6
Page 194 and 195: 186 Biographical Vignettes Figure 6
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 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
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
show all

MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Create successful ePaper yourself

Delete template?

Save as template?