Skip to main content
Log in

Triangles II: Complex triangle coordinates

  • Research Papers
  • Published:
aequationes mathematicae Aims and scope Submit manuscript

Summary

This paper is the second in a series of three examining Euclidean triangle geometry via complex cross ratios. In the first paper of the series, we examined triangle shapes. In this paper, we coordinatize the Euclidean plane using cross ratios, and use these triangle coordinates to prove theorems about triangles. We develop a complex version of Ceva's theorem, and apply it to proofs of several new theorems. The remaining paper of this series will deal with complex triangle functions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gallatly, W.,The modern geometry of the triangle. 2nd edition, Hodgson, London, 1913.

    Google Scholar 

  2. Gale, C.,From Euclid to Descartes to Mathematica to oblivion? Mathematical entertainments (column) in Math. Intelligencer14 (1992), no. 2, 68–71.

    Google Scholar 

  3. Kimberling, C.,Central points and central lines in the plane of a triangle. Math. Mag.67 (1994), 163–187.

    Google Scholar 

  4. Lester, J. A.,Triangles I: Shapes. Aequationes Math.52 (1996), 30–54.

    Google Scholar 

  5. Lester, J. A.,Trianigles III: Complex triangle functions. To appear in Aequationes Math.

  6. Rigby, J.,Napoleon revisited. J. Geom.33 (1988), 129–146.

    Google Scholar 

  7. Samaga, H.-J.,A unified approach to Miquel's theorem and its degenerations. InGeometry and differential geometry (Proc. Conf. Haifa, 1979) [Lecture Notes in Math., No. 792]. Springer, Berlin, 1980, pp. 132–142.

    Google Scholar 

  8. Schaeffer, H. andBenz, W.,Peczar-Doppelverhältnisidentitäten zum allgemeinen Satz von Miquel. Abh. Math. Sem. Hamburg42 (1974), 228–235.

    Google Scholar 

  9. Shick, J.,Beziehung zwischen Isogonalcentrik und Invariantentheorie. Bayer. Akad. Wiss. Sitzungsber.30 (1900), 249–272.

    Google Scholar 

  10. Schwerdtfeger, H.,The geometry of complex numbers. Dover, New York, 1979.

  11. Yaglom, I. M. Complex numbers in geometry. Academic Press, New York, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lester, J.A. Triangles II: Complex triangle coordinates. Aeq. Math. 52, 215–245 (1996). https://doi.org/10.1007/BF01818341

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01818341

AMS (1991) subject classification

Navigation