Journal of Graphic Science of Japan
Online ISSN : 1884-6106
Print ISSN : 0387-5512
ISSN-L : 0387-5512
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Volume 52, Issue 2
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  • The relationship between Graphic science and mathematical analysis in view of the Kakeya needle problem
    Hiroki SAITO
    2018 Volume 52 Issue 2 Pages 3-
    Published: 2018
    Released on J-STAGE: June 01, 2019
    DOIhttps://doi.org/10.5989/jsgs.52.2_3
    JOURNAL FREE ACCESS
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    　The Kakeya problem is to find the Hausdorff dimension of the Kakeya set, which is a subset in n-dimensional Euclidean space, with measure 0, containing a unit line segment in each direction. The Kakeya problem (conjecture) is that the Kakeya set must have Hausdorff dimension at least n. It was settled in the plane, n = 2, but in higher dimensions, the problem is still open. In this paper, first we describe the original Kakeya needle problem: Find the smallest area so that a unit line segment can be rotated by 180 degrees in this domain, and give an answer of this problem. It is known as a classical and geometrical problem, but recently it has realized that this type of problem is connected to modern analysis, in particular, Fourier analysis (which is also regarded as the real and harmonic analysis). In the latter half of this paper, it will be given a brief description about these problems.
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