Skip to main content
    • Aa
    • Aa

Some remarks on the Kakeya problem

  • Roy O. Davies (a1)

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.

Hide All
(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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 45 *
Loading metrics...

Abstract views

Total abstract views: 218 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.