World Geometry

  • Jan C. A. Boeyens


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.



Ideal Point Euclidean Geometry Double Point Projective Geometry Radial Line 
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  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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