## The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry TeachingCelebrating a century of geometry and geometry teaching, this book will give the reader an enjoyable insight into all things geometrical. There are a wealth of popular articles including sections on Pythagoras, the golden ratio and recreational geometry. Historical items, drawn principally from the Mathematical Gazette, are authored by mathematicians such as G. H. Hardy, Rouse Ball, Thomas Heath and Bertrand Russell as well as some more recent expositors. Thirty 'Desert Island Theorems' from distinguished mathematicians and educationalists give light to some surprising and beautiful results. Contributors include H. S. M. Coxeter, Michael Atiyah, Tom Apostol, Solomon Golomb, Keith Devlin, Nobel Laureate Leon Lederman, Carlo Séquin, Simon Singh, Christopher Zeeman and Pulitzer Prizewinner Douglas Hofstadter. The book also features the wonderful Eyeball Theorems of Peruvian geometer and web designer, Antonio Gutierrez. For anyone with an interest in mathematics and mathematics education this book will be an enjoyable and rewarding read. |

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### Contents

III | xv |

IV | 5 |

V | 16 |

VI | 23 |

VII | 25 |

VIII | 27 |

X | 29 |

XI | 34 |

LXVII | 230 |

LXIX | 232 |

LXXII | 235 |

LXXIII | 237 |

LXXV | 239 |

LXXVIII | 243 |

LXXXI | 250 |

LXXXIV | 261 |

XII | 43 |

XIV | 45 |

XVI | 63 |

XVII | 80 |

XX | 82 |

XXIII | 90 |

XXV | 105 |

XXVIII | 109 |

XXX | 120 |

XXXII | 126 |

XXXV | 136 |

XXXVI | 140 |

XXXIX | 161 |

XLI | 163 |

XLII | 165 |

XLIII | 167 |

XLIV | 175 |

XLV | 177 |

XLVIII | 181 |

L | 183 |

LI | 187 |

LII | 189 |

LIII | 199 |

LIV | 210 |

LV | 212 |

LVI | 214 |

LVII | 218 |

LX | 223 |

LXII | 224 |

LXIV | 226 |

LXXXVI | 262 |

LXXXIX | 264 |

XC | 266 |

XCII | 273 |

XCIV | 279 |

XCVII | 281 |

XCVIII | 285 |

C | 287 |

CI | 288 |

CIV | 289 |

CVII | 293 |

CX | 295 |

CXI | 300 |

CXIV | 305 |

CXVII | 314 |

CXX | 319 |

CXXII | 331 |

CXXV | 338 |

CXXVIII | 353 |

CXXIX | 355 |

CXXX | 358 |

CXXXII | 360 |

CXXXIV | 364 |

CXXXVI | 367 |

CXXXVIII | 390 |

CXLI | 393 |

CXLV | 400 |

CXLVIII | 404 |

CLI | 411 |

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### Common terms and phrases

algebra analytical geometry Archimedes axioms base calculation centre century Chasles circle colour congruent conic construction curriculum curves cyclic quadrilateral deductive Desargues Descartes Desert Island Theorems diagonal diagram dissection Doug French edges elementary elements equal equation equilateral triangle Euclid Euclidean example fact Figure Fold four Four Colour Theorem geometry teaching given golden ratio golden rectangle golden section Greek H. S. M. Coxeter ideas inscribed interesting intersection knot length line segment Math Mathematical Association Mathematical Gazette mathematicians Mathematics in School method parallel parallelogram perpendicular pieces plane player polygon Poncelet problem projective geometry proof Prop properties propositions proved Ptolemy's Theorem published in Mathematical pupils pyramid Pythagoras Pythagorean radius result right angles school geometry sequence shape sides similar solid solution space sphere sphinx square root Stage straight line surfaces symmetry tangent teachers tessellation theory triangle ABC trominoes vertex vertices