Geometry Formulas and Facts
by Silvio Levy
Publisher: CRC Press 1995
Contents: Coordinate Systems in the Plane; Plane Symmetries or Isometries; Other Transformations of the Plane; Lines; Polygons; Circles; Conics; Special Plane Curves; Coordinate Systems in Space; Space Symmetries or Isometries; Other Transformations of Space; Directions, Planes and Lines; Polyhedra; Spheres; Surfaces of Revolution. The Torus; Quadrics.
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by David Ramsay Hay - W. Blackwood and sons
From the table of contents: Nature of the science of aesthetics explained; Plane figures the bases of all forms; The isosceles triangle; Universal application of the composite ellipse in the arts of ornamental design; and more.
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Axioms were uncovered in Euclid's geometry. These discoveries were organized into a more rigorous axiomatic system by David Hilbert in his Grundlagen der Geometrie (1899) which contained his definitive set of axioms for Euclidean geometry.
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Mathematical billiards describe the motion of a mass point in a domain with elastic reflections from the boundary. Billiards is not a single mathematical theory, it is rather a mathematician’s playground where various methods are tested.
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Contents: Pythagoras' theorem; Pythagorean triples; commensurable and incommensurable quantities; Eudoxus' theory of proportion; method of exhaustion; continued fractions; the surface area of a sphere; the method; regular polyhedra; symmetries; etc.