Abstract
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.
