WebFeb 13, 2013 · The Kakeya problem was proposed in 1917, by the Japanese mathematician Soichi Kakeya. The problem states, In the class of figures in which a segment of length 1 … WebJSTOR Home
(PDF) A finite version of the Kakeya problem - ResearchGate
WebFeb 13, 2013 · The Kakeya problem was proposed in 1917, by the Japanese mathematician Soichi Kakeya. The problem states, In the class of figures in which a segment of length 1 can be turned around through 360˚, remaining always within the figure, which one has the smallest area? In this talk I will give a very brief introduction to the Kakeya problem. The Kakeya needle problem asks whether there is a minimum area of a region $${\displaystyle D}$$ in the plane, in which a needle of unit length can be turned through 360°. This question was first posed, for convex regions, by Sōichi Kakeya (1917). The minimum area for convex sets is achieved by an … See more In mathematics, a Kakeya set, or Besicovitch set, is a set of points in Euclidean space which contains a unit line segment in every direction. For instance, a disk of radius 1/2 in the Euclidean plane, or a ball of radius 1/2 … See more Besicovitch was able to show that there is no lower bound > 0 for the area of such a region $${\displaystyle D}$$, in which a needle of unit length can be turned around. That is, for every $${\displaystyle \varepsilon >0}$$, there is region of area One method of … See more Sets containing circles and spheres Analogues of the Kakeya problem include considering sets containing more general shapes than lines, such as circles. • In … See more • Nikodym set See more Statement The same question of how small these Besicovitch sets could be was then posed in higher dimensions, giving rise to a number of … See more Somewhat surprisingly, these conjectures have been shown to be connected to a number of questions in other fields, notably in harmonic analysis. For instance, in 1971, Charles Fefferman was able to use the Besicovitch set construction to show that in dimensions … See more 1. ^ Pal, Julius (1920). "Ueber ein elementares variationsproblem". Kongelige Danske Videnskabernes Selskab Math.-Fys. Medd. 2: 1–35. 2. ^ Besicovitch, Abram (1919). "Sur deux questions d'integrabilite des fonctions". J. Soc. Phys. Math. 2: … See more flik hat picture
The Kakeya Problem University of Kentucky College of Arts
WebFeb 27, 2024 · Kakeya posed the problem in 1917, and Abram Samoilovitch Besicovitch solved it in 1928, showing that there was no minimum area greater than 0. If you turn it slowly enough, over a long enough ... WebFeb 16, 2001 · New bounds on Kakeya problems. Nets Katz, Terence Tao. We establish new estimates on the Minkowski and Hausdorff dimensions of Besicovitch sets and obtain … WebMar 15, 2024 · Kakeya needle problem. The Kakeya needle problem asks whether there is a minimum area of a region in the plane, in which a needle of unit length can be turned through 360°. This question was first posed, for convex regions, by Sōichi Kakeya ().The minimum area for convex sets is achieved by an equilateral triangle of height 1 and area 1/ √ 3, as … greater brandon burlsworth movie