Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T13:26:25.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Cevian axes and related curves

Published online by Cambridge University Press:  01 August 2016

M. D. Fox  and
J. R. Goggins
M. D. Fox
Affiliation:
2 Leam Road, Leamington Spa, Warwickshire CV31 3PA e-mail: [email protected]
J. R. Goggins
Affiliation:
10 Bowling Green Road, Whiteinch, Glasgow G14 9NU
Get access Rights & Permissions [Opens in a new window]

Extract

When exploring some triangle geometry, we stumbled upon a set of Cevian axes: lines having certain properties in common with the Euler line. These axes yielded interesting results that we had not seen before. However, we have since learnt that many of them were discovered in the 19th Century. We were also unaware that John Rigby had covered much of this ground in unpublished work in the 1990s (private communication). We are therefore reluctant to claim any of our results as new, even though we hope that some may be.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 520 , March 2007 , pp. 2 - 26
Copyright
Copyright © The Mathematical Association 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References and notes

1. The Geometer’s Sketchpad (version 4), Key Curriculum Press, 1150 65th Street, Emeryville, California 94608, USA. http:// www.keypress.com Google Scholar
2. , F. G.-M., Exercices de Géométrie, Éditions Gabay, Jacques (1991), reprint of 6th edition published by Mame (Tours) andDe Gigord (Paris) (1920). (The 5th edition is accessible at http://www.hti.umich.edu/u/ umhistmath/, the author’s name being given as Marie, G.)Google Scholar
3. Loney, S. L., Coordinate Geometry, Part II, Macmillan (1930).Google Scholar
4. Sommerville, D. M. Y., Analytical Conies 3rd edn., Bell (1933).Google Scholar
5. Scott, J. A., Some examples of the use of areal coordinates in triangle geometry, Math. Gaz. 83 (November 1999) pp. 472–477.Google Scholar
6. http://perso.wanadoo.fr/bernard.gibert/index.html (This web site has the names, diagrams, equations and properties of many cubic curves associated with a triangle.)Google Scholar
7. Cundy, H. M. and Parry, C. F., Some cubic curves associated with a triangle, Journal of Geometry (Birkhäuser), 53 (1995) pp. 41–66.Google Scholar
8. Eddy, R. H. and Fritsch, R., The conies of Ludwig Kiepert; a comprehensive lesson in the geometry of the triangle, Mathematics Magazine, 67 (1994) pp. 188–205.Google Scholar
9. Leversha, Gerry and Woodruff, Paul, From triangle to hyperbola, Math. Gaz. 86 (July 2002) pp. 311–316.Google Scholar
10. Johnson, Roger A., Advanced Euclidean Geometry (Modern Geometry), Dover Publications (1960), reprint of 1st edition published by Mifflin, Houghton (1929).Google Scholar