Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T17:12:34.024Z Has data issue: false hasContentIssue false
  • English
  • Français

An extension of Holditch’s theorem on the area within a closed curve

Published online by Cambridge University Press:  01 August 2016

Mark J. Cooker
Mark J. Cooker*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ
Get access Rights & Permissions [Opens in a new window]

Extract

While reading a book by David Wells on curious and interesting geometry, I came across the following remarkable theorem named after Holditch.

In Figure 1 the point R divides a straight stick ST into lengths p and q, where p, q 0. We restrict the end points of the stick, S and T, to lie on a plane, simple, closed, convex contour, C 1, and ST slides around C1 . Assuming C 1 is such that ST can pass around C 1 once, the locus of R is another plane closed contour, C, inside C 1.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 82 , Issue 494 , July 1998 , pp. 183 - 188
Copyright
Copyright © The Mathematical Association 1998

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.)

Article purchase

Temporarily unavailable

References

1. Wells, D. The Penguin dictionary of curious and interesting geometry, Penguin (1991) p. 103.Google Scholar
2. Bender, H. The Holditch curve tracer Mathematics Magazine, (March 1981) pp. 128–129.CrossRefGoogle Scholar
3. Gunes, R. Keles, S. Closed spherical motions and Holditch’s theorem, Mechanism and Machine Theory, 29 (1994) pp. 755–758.Google Scholar
4. Hacisalihoglu, H. H. Adelbaky, R. A. Holditch’s theorem for one-parameter closed motions, Mechanism and Machine Theory, 32 (1997) pp. 235–239.Google Scholar
5. Holditch, H. Geometrical theorem, Q. J. Pure and Applied Mathematics, 2 (1858) p. 38.Google Scholar
6. Davis, R. F. Geometrical note, Math. Gaz. 12 (1924) p. 110.CrossRefGoogle Scholar
7. Heawood, P. J. The locus of one vertex of a rigid triangle whose other vertices describe fixed circles, Math. Gaz. 4 (1898) p. 108.CrossRefGoogle Scholar
8. Hardy, G. H. Pure mathematics, (10th edition), Cambridge University Press (1952) pp. 271–272.Google Scholar