Elementary GeometryAmerican Mathematical Soc., 2008 - 243 pages Plane geometry is developed from its basic objects and their properties and then moves to conics and basic solids, including the Platonic solids and a proof of Euler's polytope formula. Particular care is taken to explain symmetry groups, including the description of ornaments and the classification of isometries. |
Contents
| 1 | |
Chapter 2 Elementary geometrical figures and their properties | 9 |
Chapter 3 Symmetries of the plane and of space | 99 |
Chapter 4 Hyperbolic geometry | 167 |
Chapter 5 Spherical geometry | 209 |
| 229 | |
| 235 | |
| 237 | |
Back Cover | 244 |
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Common terms and phrases
affine mapping arbitrary point Axiom called central dilation centroid Ceva's theorem chord circumcircle collinear complex numbers composition compute cone congruent conic section consider coordinates Corollary corresponding cube curve defined denote determine dihedral group distinct points dodecahedron elementary geometry elliptic equal equation Euclidean space exactly Example finite fived point fixed point follows immediately formula fractional linear transformation Fuchsian groups glide reflection Hence hyperbolic geometry hyperbolic plane hyperbolic segment hyperbolic transformation hyperbolic triangle icosahedron image points incidence theorem inscribed angles interior angles intersection point isometry group lattice Lemma length lies limit set matrix midpoint obtain orthocenter orthogonal pair parabolic transformation parallel parameter perpendicular bisector plane reflections polygonal polytope projection Proof Prove Pythagoras quadrilateral radius real number resp right angle segment similarity transforms Simson line sphere spherical triangle Steiner line subgroup subset symmetry group tangent tetrahedron three points triangle A(A triple vertex vertices weighted centroid