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Products of lengths of line segments associated with elliptical chords

Published online by Cambridge University Press:  01 August 2016

Thomas E. Price
Thomas E. Price*
Affiliation:
Department of Theoretical and Applied Mathematics, The University of Akron, Akron, Ohio 44325, USA
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Extract

Suppose the unit circle is divided into n > 1 equal arcs and points are placed at the ends of the arcs. Choose one of these points to be the ‘base point’ and draw chords connecting each of the other points to the base point. (See Figure 1 for the case n = 8.) Then the product of the lengths of these chords equals n (see Sichardt). In a related article, Eisemann considered the product of the lengths of the (nondegenerate) perpendiculars drawn from the centre of the unit circle to these chords.

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 517 , March 2006 , pp. 13 - 20
Copyright
Copyright © The Mathematical Association 2006

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References

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