Introduction to Geometry

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