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Geometry Formulas and Facts

Silvio Levy

This document is excerpted from the 30th Edition of the   CRC Standard Mathematical Tables and Formulas, published in late 1995 by CRC press.

This completely rewritten and updated edition of CRC's classical reference work is edited by Dan Zwillinger, and boasts the participation of dozens of distinguished contributors in all fields of mathematics. Ordering information is available here.

The present excerpt covers the area of Geometry (minus differential geometry). It was written by Silvio Levy and is reproduced here with permission. All the figures were made by the author using Mathematica, except those in Section 2.4, which were made using kali.

This online version was prepared with the help of Nikos Drakos's latex2html converter; for compatibility of text and formulas, choose a largish text font with your browser.

A button in the text indicates a cross-reference.

• Part I: Two-Dimensional Geometry
  • 1 Coordinate Systems in the Plane
    • 1.1 Substitutions and Transformations
    • 1.2 Cartesian Coordinates in the Plane
    • 1.3 Polar Coordinates in the Plane
    • 1.4 Homogeneous Coordinates in the Plane
    • 1.5 Oblique Coordinates in the Plane
  • 2 Plane Symmetries or Isometries
    • 2.1 Formulas for Symmetries in Cartesian Coordinates
    • 2.2 Formulas for Symmetries in Homogeneous Coordinates
    • 2.3 Formulas for Symmetries in Polar Coordinates
    • 2.4 Wallpaper Groups
  • 3 Other Transformations of the Plane
    • 3.1 Similarities
    • 3.2 Affine Transformations
    • 3.3 Projective Transformations
  • 4 Lines
    • 4.1 Distances
    • 4.2 Angles
    • 4.3 Concurrence and Collinearity
  • 5 Polygons
    • 5.1 Triangles
    • 5.2 Quadrilaterals
    • 5.3 Regular Polygons
  • 6 Circles
  • 7 Conics
    • 7.1 Alternative Characterization
    • 7.2 The General Quadratic Equation
    • 7.3 Additional Properties of Ellipses
    • 7.4 Additional Properties of Hyperbolas
    • 7.5 Additional Properties of Parabolas
  • 8 Special Plane Curves
    • 8.1 Algebraic Curves
    • 8.2 Roulettes (Spirograph Curves)
    • 8.3 Spirals
    • 8.4 The Peano Curve and Fractal Curves
• Part II: Three-Dimensional Geometry
  • 9 Coordinate Systems in Space
    • 9.1 Cartesian Coordinates in Space
    • 9.2 Cylindrical Coordinates in Space
    • 9.3 Spherical Coordinates in Space
    • 9.4 Relations between Cartesian, Cylindrical, and Spherical Coordinates
    • 9.5 Homogeneous Coordinates in Space
  • 10 Space Symmetries or Isometries
    • 10.1 Formulas for Symmetries in Cartesian Coordinates
    • 10.2 Formulas for Symmetries in Homogeneous Coordinates
  • 11 Other Transformations of Space
    • 11.1 Similarities
    • 11.2 Affine Transformations
    • 11.3 Projective Transformations
  • 12 Directions, Planes and Lines
    • 12.1 Direction Angles and Direction Cosines
    • 12.2 Planes
    • 12.3 Lines
  • 13 Polyhedra
    • 13.1 Regular Polyhedra
    • 13.2 Cylinders
    • 13.3 Cones
  • 14 Spheres
  • 15 Surfaces of Revolution. The Torus
  • 16 Quadrics

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Silvio Levy
Wed Oct 4 16:41:25 PDT 1995

This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas (CRC Press). Unauthorized duplication is forbidden.