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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
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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

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References

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