Introduction to Geometry

ISBN-13: 9780471504580 / Angielski / Miękka / 1991 / 496 str.

H. S. M. Coxeter;Coxeter

Opis

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

Spis treści

Triangles.

Regular Polygons.

Isometry in the Euclidean Plane.

Two–Dimensional Crystallography.

Similarity in the Euclidean Plane.

Circles and Spheres.

Isometry and Similarity in Euclidean Space.

Coordinates.

Complex Numbers.

The Five Platonic Solids.

The Golden Section and Phyllotaxis.

Ordered Geometry.

Affine Geometry.

Projective Geometry.

Absolute Geometry.

Hyperbolic Geometry.

Differential Geometry of Curves.

The Tensor Notation.

Differential Geometry of Surfaces.

Geodesics.

Topology of Surfaces.

Four–Dimensional Geometry.

Tables.

References.

Answers to Exercises.

Index.