Introduction to geometry
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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ISOMETRY IN THE EUCLIDEAN PLANE
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absolute geometry affine affine geometry asymptotic triangle axes Axiom axis barycentric coordinates called Cartesian coordinates central inversion circle of Apollonius circle with center circumcenter common point congruent conic Coxeter curvature curve deduce derived diagonal dilatation dilative reflection dilative rotation distance distinct edges elliptic equal equation equilateral Euclid EXERCISES expressed faces Figure finite four fundamental region geometry given circles glide reflection half-turn Hence horocycle hyperbolic infinite integers invariant point inversive plane joining lattice points locus Mathematical meet midpoint mirrors notation obtain octahedron opposite isometry orthogonal pairs parallel lines parallelogram pencil perpendicular Platonic solids point at infinity points of intersection polygon positive product of reflections projective plane proof prove quadrangle quadric radius ratio rays regular right angles Schlegel diagram segment sides similarity sphere square surface symmetry group tangent tessellation tetrahedron theorem tion transformation translation triangle ABC vector vertex vertices