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On the Steinhaus billiard table problem

Published online by Cambridge University Press:  24 October 2008

H. T. Croft  and
H. P. F. Swinnerton-Dyer
H. T. Croft
Affiliation:
Peterhouse, Cambridge, and Trinity College, Cambridge
H. P. F. Swinnerton-Dyer
Affiliation:
Peterhouse, Cambridge, and Trinity College, Cambridge
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Extract

Let be a plane closed convex curve, and regard as the boundary of a billiard table. If a perfectly elastic billiard ball is set moving on the table, its path will be a polygon inscribed in ; and this will be closed if and only if the motion is periodic. We seek periodic paths which are triangles.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 37 - 41
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Nemytskii, V. V. and Stepanov, V. V.Qualitative theory of differential equations (English translation, Princeton, 1960).Google Scholar
(2)Steinhaus, H.New Scottish Book, Problem 335.Google Scholar