This volume attempts to revitalize the sadly neglected topic of geometry. Apart from the general emphasis on the idea of transformation and on the desirability of spending some time in such unusual environments as affine space and absolute space, the chief novelties of the text are a simple treatment of the orthocenter, the use of dominoes to illustrate six of the seventeen space groups of two-dimensional crystallography, a construction for the invariant point of a dilative reflection, a description of the general circle-preserving transformation and the spiral similarity. The book also includes an 'explanation' of phyllotaxis, an 'ordered' treatment of Sylvester's problem, an economical system of axioms for affine geometry, an 'absolute' treatment of rotation groups, an elementary treatment of the horosphere and the extreme ternary quadratic form. The author describes the correction of a prevalent error concerning the shape of the monkey saddle, an application of
This volume attempts to revitalize the sadly neglected topic of geometry. Apart from the general emphasis on the idea of transformation and on the desirability of spending some time in such unusual environments as affine space and absolute space, the chief novelties of the text are a simple treatment of the orthocenter, the use of dominoes to illustrate six of the seventeen space groups of two-dimensional crystallography, a construction for the invariant point of a dilative reflection, a description of the general circle-preserving transformation and the spiral similarity. The book also includes an 'explanation' of phyllotaxis, an 'ordered' treatment of Sylvester's problem, an economical system of axioms for affine geometry, an 'absolute' treatment of rotation groups, an elementary treatment of the horosphere and the extreme ternary quadratic form. The author describes the correction of a prevalent error concerning the shape of the monkey saddle, an application of
Part I
Triangles 3
Regular Polygons 26
Isometry in the Euclidean Plane 39
Two-Dimensional Crystallography 50
Similarity in the Euclidean Plane 67
Circles and Spheres 77
Isometry and Similarity in Euclidean Space 96
Part II
Coordinates 107
Complex Numbers 135
The Five Platonic Solids 148
The Golden Section and Phyllotaxis 160
Part III
Ordered Geometry 175
Affine Geometry 191
Projective Geometry 229
Absolute Geometry 263
Hyperbolic Geometry 287
Part IV
Differential Geometry of Curves 307
The Tensor Notation 328
Differential Geometry of Surfaces 342
Geodesics 366
Topology of Surfaces 379
Four-Dimensional Geometry 396
Tables 413
References 415
Answers to Exercises 419
Index 459
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC was a British-born Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London, received his BA and PhD from Cambridge, but lived in Canada from age 29.
 |
Ask a Question About this Product More... |
|
