Advertisement

Journal of Geometry

, Volume 33, Issue 1–2, pp 129–146 | Cite as

Napoleon revisited

  • J. F. Rigby
Article

Abstract

Napoleon's Theorem can be neatly proved using a tessellation of the plane. The theorem can be generalized by using three similar triangles (instead of the three equilateral triangles) erected in different ways on the three sides of the triangle. Various interesting special cases occur.

Keywords

Equilateral Triangle Interesting Special Case Similar Triangle 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    BACHMANN, F.:Aufbau der Geometrie aus dem Spiegelungsbegriff, Springer, Berlin 1959, 1973.Google Scholar
  2. [2]
    COOLIDGE, J. L.:A Treatise on the Circle and the Sphere, Oxford University Press 1916.Google Scholar
  3. [3]
    COXETER, H. S. M.:Introduction to Geometry, 2nd ed., Wiley, New York 1969.Google Scholar
  4. [4]
    COXETER, H. S. M. and GREITZER, S. L.:Geometry Revisited, Mathematical Association of America, Washington DC, 1967.Google Scholar
  5. [5]
    NEUMANN, B. H.:Some remarks on polygons, J. London Math. Soc.16 (1941), 230–245.Google Scholar

Copyright information

© Birkhäuser Verlag 1988

Authors and Affiliations

  • J. F. Rigby
    • 1
  1. 1.Department of Pure MathematicsUniversity CollegeCardiffWales UK

Personalised recommendations