Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T11:23:21.606Z Has data issue: false hasContentIssue false

On the Steinhaus billiard table problem

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1963

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.)

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