Mathematical Notes

  • E. F. Beckenbach
  • Karl Menger


In the geometry of our ordinary plane, points and lines play different rôles. There exist parallel lines, that is, lines which are not on a common point. In fact, for any given line l, there exists exactly one parallel line on every point which is not on l But there are no parallel points, in the sense of points which are not on a common line. Every two distinct points are on exactly one common line.


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    Ergebn. math. Kolloquiums, vol. 8 (1937), 25 and Alt, loc. cit.3Google Scholar

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • E. F. Beckenbach
    • 1
    • 2
  • Karl Menger
    • 3
  1. 1.University of CaliforniaLos Angeles 24USA
  2. 2.Institute for Numerical Analysis of the National Bureau of StandardsUSA
  3. 3.Illinois Institute of TechnologyUSA

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