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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

1. Sichardt, M., Ein satz vom kries, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 34 (1954) p. 429.Google Scholar
2. Eisemann, K., Extension of a theorem about the circle, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 52 (1972) pp. 496–497.CrossRefGoogle Scholar
3. Price, T. E., Product of chord lengths of an ellipse, Mathematics Magazine 75, (4) (2002) pp. 300–307.Google Scholar
4. Usiskin, Z., Products of sines, Two-Year College Mathematics Journal 10 (5) (1979) pp. 334–340.CrossRefGoogle Scholar
5. Usiskin, Z., person note by email, 2002.Google Scholar
6. Mazzoleni, A. P. and Shen, S. S., The product of chord lengths of a circle, Mathematics Magazine 68 (1) (1995) pp. 59–60.CrossRefGoogle Scholar
7. Lewis, B., Power Chords, Math. Gaz. 86 (July 2002) p. 233.Google Scholar
8. Price, T. E., Products of elliptical chord lengths and the Fibonacci numbers, Fibonacci Quarterly, 2 (2) (2005) pp. 149–156.Google Scholar
9. Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York (2001).Google Scholar