Advertisement

The Mathematical Intelligencer

, Volume 22, Issue 1, pp 54–59 | Cite as

A fourfold point of concurrence lying on the Euler line of a triangle

  • Michael Longuet-Higgins
Article
  • 106 Downloads

Keywords

Mathematical Intelligencer Median Point Notable Point Real Projective Plane Euler Line 
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.
    N. Altshiller-Court, “On the de Longchamps circle of a triangle,”Am. Math. Monthly 33 (1926), 638–375.Google Scholar
  2. 2.
    N. Altshiller-Court,College Geometry, Barnes and Noble, Inc. New York, 1952.MATHGoogle Scholar
  3. 3.
    J.L. Coolidge,A Treatise on the Circle and the Sphere, Chelsea, New York, 1971.MATHGoogle Scholar
  4. 4.
    H.S.M. Coxeter,The Real Projective Plane, 2nd ed., Cambridge University Press, Cambridge, 1955.MATHGoogle Scholar
  5. 5.
    H.S.M. Coxeter, “Some applications of trilinear coordinates,”Linear Alg. Appl. 226-228 (1995), 375–388.CrossRefMathSciNetGoogle Scholar
  6. 6.
    G. de Longchamps, “Sur un nouveau cercle remarquable,”J. Math. Spéciales 58 (1886) 57–60, 83–87, 100–104, and 126–128.Google Scholar
  7. 7.
    L. Euler, “Solutio facilis problematum quorumdam geometricorum difficillimorum,“Novi Comment” Acad. Imp. Sei. Petropolitanae 11 (1765, published 1767), 103–123. For an English abstract by J.S. Mackay, seeProc. Edin Math. Soc. 4 (1886), 51–55.Google Scholar
  8. 8.
    A. Gob, “Sur la droite et le cercle d’Euler,”Mathesis(1889) Supplement, 1-2.Google Scholar
  9. 9.
    D.R. Hofstadter, “Discovery and dissection of a geometric gem,”Geometry Turned On!, ed. by J.R. King and D. Schattschneider, Mathematical Association of America, Washington, DC, 1997, pp. 3–14.Google Scholar
  10. 10.
    W.P. Milne,Homogeneous Coordinates, Edward Arnold, London, 1924.Google Scholar
  11. 11.
    C. Nagel,Untersuchungen über die Wichtigsten zum Dreiecke Gehörigen Kreise, Mohler’schen Buchhandlung im Ulm, Leipzig 1836.Google Scholar
  12. 12.
    M. Simon,Über die Entwicklung der Elementar-Geometrie im XIX Jahrhundert, Teubner, Leipzig, 1906, pp. 124–141.Google Scholar
  13. 13.
    G. Spieker, “Ein merkwürdiger Kreis um den Schwerpunkt des Perimeters des geradlinigen Dreiecks als Analogen des Kreises der neun Punkte,”Grunert’s Arch. 51 (1870), 10–14.MATHGoogle Scholar
  14. 14.
    E. Vigarié, “La bibliographie de la géométrie du triangle,”C.R. Fr. Avance. Sci. 2 (1895), 50–63.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2000

Authors and Affiliations

  • Michael Longuet-Higgins
    • 1
  1. 1.Institute of Nonlinear ScienceUniversity of California La JollaLa JollaUSA

Personalised recommendations