Introduction to Geometry

ABCD absolute geometry affine geometry asymptotic triangle axes Axiom axis barycentric coordinates called centroid circle with center collinear points complete quadrangle congruent conic Coxeter cube curvature curve deduce derived diagonal dilatation direct distance edges elliptic equal equation equilateral Euclid Euclidean EXERCISES expressed faces Figure finite four fundamental region given glide reflection half-turn Hence horocycle hyperbolic infinite integers invariant point inversive plane isometry joining lattice points locus Mathematical meet midpoints mirrors notation obtain octahedron opposite isometry ordered geometry orthogonal P₁ pairs parallel lines parallelogram pencil perpendicular phyllotaxis Platonic solids polygon positive projective plane proof prove quadrangle quadric r₁ radius ratio rays regular right angles rotation segment sides space sphere spiral similarity surface symmetry group t₁ tangent tessellation tetrahedron theorem tion transforms translation triangle ABC vector vertex vertices ΣΣ