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Some remarks on the Kakeya problem

Published online by Cambridge University Press:  24 October 2008

Roy O. Davies
Roy O. Davies
Affiliation:
The University, Leicester
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Extract

Besicovitch's construction(1) of a set of measure zerot containing an infinite straight line in every direction was subsequently adapted (2, 3, 4) to provide the following answer to Kakeya's problem (5): a unit segment can be continuously turned round, so as to return to its original position with the ends reversed, inside an arbitrarily small area. The last word on Kakeya's problem itself seems to be F. Cunningham Jr.'s remarkable result(6)‡ that this can be done inside a simply connected subset of arbitrarily small measure of a unit circle.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 3 , May 1971 , pp. 417 - 421
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

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