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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Fraser, Robert 2016. KAKEYA-TYPE SETS IN LOCAL FIELDS WITH FINITE RESIDUE FIELD. Mathematika, Vol. 62, Issue. 02, p. 614.


    Lutz, Jack H. and Lutz, Neil 2015. Lines missing every random point1. Computability, Vol. 4, Issue. 2, p. 85.


    Murphy, Brendan and Pakianathan, Jonathan 2015. Kakeya configurations in Lie groups and homogeneous spaces. Topology and its Applications, Vol. 180, p. 1.


    Dummit, Evan P. and Hablicsek, Márton 2013. KAKEYA SETS OVER NON-ARCHIMEDEAN LOCAL RINGS. Mathematika, Vol. 59, Issue. 02, p. 257.


    Füredi, Zoltán and Wetzel, John E. 2011. Covers for closed curves of length two. Periodica Mathematica Hungarica, Vol. 63, Issue. 1, p. 1.


    Molter, Ursula and Rela, Ezequiel 2010. Improving dimension estimates for Furstenberg-type sets. Advances in Mathematics, Vol. 223, Issue. 2, p. 672.


    Rogers, C. A. 1988. Dimension prints. Mathematika, Vol. 35, Issue. 01, p. 1.


    Marstrand, J. M. 1979. Packing smooth curves in Rq. Mathematika, Vol. 26, Issue. 01, p. 1.


    Marstrand, J. M. 1979. Packing planes in 3. Mathematika, Vol. 26, Issue. 02, p. 180.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 69, Issue 3
  • May 1971, pp. 417-421

Some remarks on the Kakeya problem

  • Roy O. Davies (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100046867
  • Published online: 24 October 2008
Abstract

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.

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(2)A. S. Besicovitch On Kakeya's problem and a similar one. Math. Z. 27 (1928), 312320.

(3)O. Perron Über emen Satz von Besicovitch. Math. Z. 28 (1928), 383386.

(4)A. S. Besicovitch The Kakeya problem. Amer. Math. Monthly 70 (1963), 697706.

(8)J. R. Kinney A thin set of circles. Amer. Math. Monthly 75 (1968), 10771081.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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