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Adventitious quadrangles: a geometrical approach

Published online by Cambridge University Press:  22 September 2016

J. F. Rigby
J. F. Rigby*
Affiliation:
Department of Pure Mathematics, University College, P.O. Box 78, Cardiff CF11XL
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A quadrangle has four vertices, of which no three are collinear, and six sides joining the vertices in pairs. If the angle between each pair of the six sides is an integral multiple of π/n radians, n being an integer, the quadrangle is said to be n-adventitious [1]. A quadrangle is adventitious if it is n- adventitious for some n. For example, the quadrangle BCDE in Fig. 1 (the original adventitious quadrangle from which all the discussion started in [1]) is 18-adventitious. Various problems are posed in [1]; in a suitably generalised form these problems can be summarised as: find all adventitious quadrangles and prove their existence by elementary geometry.

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Type
Research Article
Information
The Mathematical Gazette , Volume 62 , Issue 421 , October 1978, pp. 183 - 191
Copyright
Copyright © Mathematical Association 1978

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References

1. Tripp, C. E., Adventitious angles, Mathl Gaz. 59, 98–106 (No. 408, June 1975).Google Scholar
2. Quadling, D. A. (editor), The adventitious angles problem: a progress report, Mathl Gaz. 61, 55–58 (No. 415, March 1977).Google Scholar
3. Rigby, J. F., Multiple intersections of diagonals of regular polygons, and related topics, Geom. Dedicata (to appear).Google Scholar
4. Bol, G., Beantwoording van prijsvraag no. 17, Nieuw Archf Wisk. (2) 18, 14–66 (1936).Google Scholar
5. Quadling, D. A. (editor), Last words on adventitious angles, Mathl Gaz. 62, 174–183 (No. 421, October 1978).Google Scholar