Geometry and the Imagination

algebraic analytic angles axes axioms axis boundary called centers of rotation centers of similitude circle circular closed curve cone configuration conformal mapping congruent conics connectivity consider construction contains corresponding cube cylinder defined Desargues discontinuous groups distance edges ellipse ellipsoid elliptic geometry equal equivalent Euclidean plane example F₁ faces figure finite fixed point follows Gaussian curvature geodesic geodesic lines given groups of motions Hence heptahedron hexagon hyperbolic plane hyperboloid incidence lattice points mean curvature minimal surface Möbius strip move obtained octahedron parabolic points parallel pass perpendicular point of intersection pointers polygon polyhedron position problem projective plane proved quadrics radius region Reye's configuration rigid motions ruled surfaces segment sides sphere spherical image square straight lines surface of revolution symmetry systems of points tangent plane tetrahedron theorem theory three-dimensional tion topological torus translation triangles umbilical points unit cell vertex vertices