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On a problem of Steinhaus about polygons

Published online by Cambridge University Press:  24 October 2008

H. T. Croft  and
M. Fowler
H. T. Croft
Affiliation:
St John's CollegeCambridge
M. Fowler
Affiliation:
St John's CollegeCambridge
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Extract

We solve a problem of Steinhaus (New Scottish Book, Problem 328; also Colloq. Math. 5 (1958), Problem 225); if p is a prime, does there exist a regular p-gon such that three of its diagonals cut in a point? The answer is in the negative, except in the case where the said diagonals are all parallel, which can clearly occur for any p ≥ 7.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 686 - 688
Copyright
Copyright © Cambridge Philosophical Society 1961

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