Sōichi Kakeya

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Sōichi Kakeya ( Japanese 掛 谷 宗 一 , Kakeya Sōichi ; born January 18, 1886 in Hiroshima Prefecture ; † January 9, 1947 ) was a Japanese mathematician, known for the Kakeya problem. Kakeya studied at the Tokyo Imperial University and taught at the Tōhoku Imperial University and the Tokyo University of Education . From 1935 he was a professor at the Imperial University of Tokyo and from 1944 director of the Statistics Institute.

In 1917, Kakeya set the task of finding the minimum surface in the plane on which a needle of length one can be rotated continuously. In 1928 Besikowitsch published the proof that the surface area can be arbitrarily small. Besikovich had already solved a similar problem in 1917 without knowledge of Kakeya's work (published in a Russian magazine in 1920). The problem has applications in different areas of mathematics from analysis to combinatorics and number theory and generalizations of the Kakeya problem are still partially open today, such as the Kakeya conjecture : a Besikowitsch set (which contains a unit needle in every orientation) in the n- dimensional Euclidean space has at least Hausdorff dimension n (open to n greater than or equal to 3).

Kakeya is also known for the theorem of Kakeya (1912/13) and Gustav Eneström (1893): a polynomial of the nth degree with real coefficients has its roots in the unit disk in the complex plane.

In 1934 he was admitted to the Japan Academy , whose Imperial Prize he received in 1928.

Individual evidence

  1. ↑ 掛 谷 宗 一 . In: デ ジ タ ル 版 日本人 名 大 辞典 + plus . January 20, 2009, Retrieved September 23, 2010 (Japanese).
  2. ↑ Some problems on maximum and minimum regarding ovals , Tohoku Science Reports, Volume 6, 1917, pp. 71-88
  3. ↑ Besicovitch On Kakeyas Problem and a similar one , Math. Zeitschrift Vol. 27, 1928, 312 ( Memento of the original from July 11, 2012 in the web archive archive.today ) Info: The archive link was automatically inserted and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. . Also, Besicovitch The Kakeya Problem , American Mathematical Monthly, Volume 70, 1963, p. 697 @1@ 2Template: Webachiv / IABot / gdz.sub.uni-goettingen.de
  4. ↑ Terence Tao From rotating needles to stability of waves , Notices AMS, Vol. 48, 2001, No. 3, pdf
  5. ↑ Represented in Edmund Landau representation and justification of some recent results of the function theory , Springer 1916 with a correction to Adolf Hurwitz's theorem
personal data
SURNAME Kakeya, Sōichi
ALTERNATIVE NAMES 掛 谷 宗 一 (Japanese)
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH January 18, 1886
PLACE OF BIRTH Hiroshima Prefecture
DATE OF DEATH January 9, 1947