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aequationes mathematicae

, Volume 45, Issue 2–3, pp 127–152 | Cite as

Functional equations associated with triangle geometry

  • Clark Kimberling
Research Papers

Summary

Triangle geometry is treated in the context of functional equations of three variablesa, b, c which may be regarded as the sidelengths of a variable triangle. Trianglecenters (e.g., incenter, circumcenter, centroid), andcentral lines (e.g., the Euler line) are defined and partitioned into classes:0-centers, 1-centers, 2-centers and0-lines, 1-lines, and 2-lines. Criteria for parallelism, perpendicularity, and other geometric relations are proved in terms of these classes. The Euler line and central lines parallel or perpendicular to the Euler line serve as examples.

AMS (1991) subject classification

Primary 39B40, 51N20 

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References

  1. [1]
    Carr, G. S.,Formulas and theorems in Pure Mathematics, 2nd ed., Chelsea, New York, 1970.Google Scholar
  2. [2]
    Eves, H. andKimberling, C. H.,Isogonal and isotomic conjugates. Amer. Math. Monthly93 (1986), 132–133.Google Scholar
  3. [3]
    Kimberling, C. H.,Central points and central lines in the plane of a triangle, to appear in Math. Magazine.Google Scholar

Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • Clark Kimberling
    • 1
  1. 1.Department of MathematicsUniversity of EvansvilleEvansvilleUSA

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