Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-13T18:40:21.463Z Has data issue: false hasContentIssue false
  • English
  • Français

The power of a point for some real algebraic curves

Published online by Cambridge University Press:  01 August 2016

Bogdan D. Suceavă ,
Adrian Vajiac  and
Mihaela B. Vajiac
Bogdan D. Suceavă
Affiliation:
Department of Mathematics, California State University Fullerton, P.O. Box 6850, Fullerton, CA 92834-6850, USA, e-mail: bsuceava@fullerton.edu
Adrian Vajiac
Affiliation:
Department of Mathematics and Computer Science, Chapman University, One University Drive, Orange, CA 92866, USA, e-mail: avajiac@chapman.edu
Mihaela B. Vajiac
Affiliation:
Department of Mathematics and Computer Science, Chapman University, One University Drive, Orange, CA 92866, USA, e-mail: avajiac@chapman.edu
Get access Rights & Permissions [Opens in a new window]

Extract

According to various sources (e.g. [1, p. 102]), the terminology of the power of a point with respect to a circle is due to Steiner. His definition appears in most classical and contemporary geometry textbooks (to mention just a few references, see [2, 3, 4, 5]). The concept of the power of a point has been revisited not only in advanced Euclidean geometry, but also in computational geometry and other areas of mathematics.

In the current literature there are two different definitions of the power of a point with respect to a circle, which we study in detail in section 2. In the first half of the twentieth century there have been published several attempts to generalise the concept of power of the point to real algebraic curves.

Type
Articles
Information
The Mathematical Gazette , Volume 92 , Issue 523 , March 2008 , pp. 22 - 28
Copyright
Copyright © The Mathematical Association 2008

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

1. F.G.-M., Exercices de géométrie, (6me édn.), Paris (1920).Google Scholar
2. Audin, M., Geometry, Springer-Verlag (2003).Google Scholar
3. Coxeter, H.S.M. and Greitzer, S.L., Geometry revisited, Yale University Press (1967).CrossRefGoogle Scholar
4. Greenberg, M.J., Euclidean and Non-Euclidean geometries, history and development, W. E. Freeman Co. (2002).Google Scholar
5. Venema, G.A., Foundations of geometry, Pearson Prentice Hall (2005).Google Scholar
6. Kaufmann, S., On Some Algebraic Curves (in Romanian), Gazeta matematică, 1916, No.6; in: Gazeta matematică, electronic archive: Softwin 2005.Google Scholar
7. Loeffler, A., Sur la puissance d’un point par rapport à une conique, Elem. Math. 18 no. 2 (1963), pp. 25–28.Google Scholar
8. Neville, E.H., The power of a point for a curve, Math. Gaz. 40 (March 1956) pp. 11–14.CrossRefGoogle Scholar
9. Andreescu, T. and Gelca, R., Mathematical Olympiad challenges, Birkhäuser (2000).CrossRefGoogle Scholar
10. Durell, C.V., Modern geometry, Macmillan, London (1920).Google Scholar
11. Moses, P.J., Circles and triangle centers associated with the Lucas circles, Forum Geometricorum, 5 (2005), pp. 97–106.Google Scholar