MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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86 Applications Figure 3.11: Warren Truss [63] combines strength with economy of materials and can therefore be relatively light. It is an improvement of the Neville truss which employs a spacing configuration of isosceles triangles. The first bridge designed in this way was constructed at London Bridge Station in 1850. Application 12 (Flammability Diagram). Flammability diagrams [334] show the regimes of flammability in mixtures of fuel, oxygen and an inert gas (typically nitrogen). The flammability diagram for methane appears in Figure 3.12. Prominent features are the air-line together with its intersections with the flammability region which determine the upper (UEL=upper explosive limit) and lower (LEL=lower explosive limit) flammability limits of methane in air. The nose of the flammability envelope determines the limiting oxygen concentration (LOC) below which combustion cannot occur. Application 13 (Goethe’s Color Triangle). In the Goethe Color Triangle [145], the vertices of an equilateral triangle are labeled with the three primary pigments, blue (A), yellow (B) and red (C). The triangle is then further subdivided as in Figure 3.13 with the subdivisions grouped into primary (I), secondary (II) and tertiary (III) triangles/colors. The secondary triangle colors represent the mix of the two adjacent primary triangle colors and the tertiary triangle colors represent the mix of the adjacent primary color triangle and the non-adjacent secondary triangle color. Goethe’s color psychology asserted that this triangle was a diagram of the human mind and he associated each of its colors with a human emotion. Subregions of the triangle are thus representative of a corresponding emotional state.
Applications 87 Figure 3.12: Flammability Diagram [334] I−C BLUE I−A II−A II−B III−C III−A II−C RED YELLOW III−B Figure 3.13: Goethe’s Color Triangle [145] I−B
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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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34 Mathematical Properties Figure 2
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Page 46 and 47: 38 Mathematical Properties 2.14(b)
Page 48 and 49: 40 Mathematical Properties - Combin
Page 52 and 53: 44 Mathematical Properties be the s
Page 64 and 65: 56 Mathematical Properties (a) (b)
Page 66 and 67: 58 Mathematical Properties Property
Page 80 and 81: 72 Mathematical Properties The best
Page 82 and 83: 74 Mathematical Properties in colum
Page 86 and 87: Chapter 3 Applications of the Equil
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Page 100 and 101: 92 Applications (a) (b) Figure 3.20
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Page 106 and 107: 98 Applications (a) Figure 3.28: Na
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Page 110 and 111: 102 Applications The eigenstructure
Page 112 and 113: 104 Mathematical Recreations Figure
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Page 120 and 121: 112 Mathematical Recreations of pla
Page 128 and 129: 120 Mathematical Recreations and n
Page 132 and 133: 124 Mathematical Recreations (a) Fi
Page 136 and 137: 128 Mathematical Recreations Recrea
Page 138 and 139: 130 Mathematical Competitions Probl
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136 Mathematical Competitions Probl
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142 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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180 Biographical Vignettes and Recr
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182 Biographical Vignettes meeting)
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184 Biographical Vignettes Figure 6
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186 Biographical Vignettes Figure 6
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Appendix A Gallery of Equilateral T
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190 Gallery Figure A.8: ET Wing Fig
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192 Gallery Figure A.18: ET Bowling
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194 Gallery Figure A.28: ET Escher
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196 Gallery Figure A.36: ET Street
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198 Gallery Figure A.44: ET Tragedy
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200 Bibliography [12] J. Aubrey, Br
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202 Bibliography [42] R. Calinger,
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204 Bibliography [74] J.-P. Delahay
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206 Bibliography [106] J. A. Flint,
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208 Bibliography [138] M. Gardner,
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210 Bibliography [169] H. Hellman,
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212 Bibliography [199] M. Kraitchik
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214 Bibliography [229] T. H. O’Be
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216 Bibliography [260] B. Russell,
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218 Bibliography [290] S. K. Stein,
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220 Bibliography [319] A. Weil, Num
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222 Index Barbier’s Theorem 56 ba
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224 Index Cruise, Tom 24 Crusades 2
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226 Index ture 157 Fermat’s Princ
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228 Index house (triangular) 197 Hu
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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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MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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