Journal of Geometry

, Volume 53, Issue 1–2, pp 41–66

Some cubic curves associated with a triangle

  • Henry Martyn Cundy
  • Cyril Frederick Parry
Article

Abstract

There are many interesting cubic curves which arise from the geometry of the triangle. In particular, those which are invariant under the operation of isogonal conjugacy have attracted much attention, and a class of these is here investigated by a variety of methods.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    COXETER, H.S.M.: Cubic Curves related to a Quadrangle,C.R.Math. Rep.Acad.Sci. Canada XV (1993), 237 - 242.Google Scholar
  2. [2]
    CUNDY, H.M.: Reflections on reflections,Math.Gaz. 58 (1974), 265 - 272.Google Scholar
  3. [3]
    DEAUX, R.:Introduction to the Geometry of Complex Numbers, F.Ungar, New York, 1956.Google Scholar
  4. [4]
    DEAUX, R.:Mathesis 1959, 228.Google Scholar
  5. [5]
    JOHNSON, R.A.:Advanced Euclidean Geometry, 1929, reprinted Dover 1960.Google Scholar
  6. [6]
    MORLEY, F. & MORLEY F.V.:Inversive Geometry, Bell, London, 1933.Google Scholar
  7. [7]
    NEUBERG, J.: Mémoire sur le tétraèdre, Supplément V,Mathesis 1885.Google Scholar
  8. [8]
    PEDOE, D.:A Course of Geometry for Colleges and Universities, Cambridge University Press, Cambridge, 1970.Google Scholar
  9. [9]
    ROBSON, A.:An Introduction to Analytical Geometry, Volume II, Cambridge University Press, Cambridge, 1947.Google Scholar
  10. [10]
    RUBIO, P.: Cubic lines relative to a triangle,J.Geom. 34 (1989), 152 - 171.Google Scholar
  11. [11]
    RUBIO, P.: Analagmatic (sic) cubics through quadratic involutive transformations,J.Geom. 48 (1993), 184–205.Google Scholar
  12. [12]
    ZWIKKER, C.:The Advanced Geometry of Plane Curves and their Applications, Dover, 1963.Google Scholar

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Henry Martyn Cundy
    • 1
  • Cyril Frederick Parry
    • 2
  1. 1.KendalUK
  2. 2.ExmouthUK

Personalised recommendations