This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self--contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4--color map problem, and provides answers to most of the exercises.
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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
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.
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