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Dual generalisations of Van Aubel’s theorem

Published online by Cambridge University Press:  01 August 2016

Michael de Villiers
Michael de Villiers*
Affiliation:
Faculty of Education, University of Durban-Westville, South Africa, e-mail: mdevilli@pixie.udw.ac.za
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Extract

In Euclidean plane geometry there exists an interesting, although limited, duality between the concepts angle and side, similar to the general duality between points and lines in projective geometry. Perhaps surprisingly, this duality occurs quite frequently and is explored fairly extensively in.

The square is self-dual regarding these concepts as it has all angles are equal, as well as all its sides.

Type
Articles
Information
The Mathematical Gazette , Volume 82 , Issue 495 , November 1998 , pp. 405 - 412
Copyright
Copyright © The Mathematical Association 1998

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References

1. de Villiers, M., Some adventures in euclidean geometry, University of Durban-Westville, Durban, South Africa (1996).Google Scholar
2. DeTemple, D., Harold, S., A round-up of square problems Mathematics Magazine, 16 (February 1996) pp. 15–27.Google Scholar
3. de Villiers, M., The role of proof in investigative, computer-based geometry: some personal reflections, in King, J. and Schattschneider, D. (eds.), Geometry turned on, MAA (1997).Google Scholar