World Geometry

Chapter

Abstract

Modern geometry developed from the work of Euclid which gave rise to two self-contained geometries, known as absolute geometry and affine geometry. Euclidean geometry depends on five postulates:
  1. 1.

    A straight line may be drawn from any point to any other point.

     
  2. 2.

    A finite straight line may be extended continuously in a straight line.

     
  3. 3.

    A circle may be described with any centre and any radius.

     
  4. 4.

    All right angles are equal to each other.

     
  5. 5.

    If a straight line meets two other straight lines so as to make the two interior angles on one side of it together less than two right angles, the other straight lines, if extended indefinitely, will meet on that side on which angles are less than two right angles.

     

Keywords

Ideal Point Euclidean Geometry Double Point Projective Geometry Radial Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Coxeter, H.S.M. (1998): Introduction to Geometry, 2nd ed., Wiley, N.Y.Google Scholar
  2. Flegg, H.G. (1974): From Geometry to Topology, Reprinted 2001, Dover, Mineola, NY.Google Scholar
  3. Jennings, G.A. (1994): Modern Geometry with Applications, Springer, N.Y.CrossRefGoogle Scholar
  4. Lee, J.M. (1997): Riemannian Manifolds, Springer, N.Y.Google Scholar
  5. Veblen, O. & J.W. Young (1910): Projective Geometry, Vol.I, 1910; Vol.II (O. Veblen sole author), 1918, Ginn and Co., Boston.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. ChemistryUniversity of PretoriaPretoriaSouth Africa

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