#Math101 Session 42

Time：Nov. 5, 2026, 13:30-15:30

Location：Online via Tencent Meeting (ID: 927-712-396)

Speaker：Mr. Sun, Ruichen (Class of 2023)

Title：The classical construction of two-dimensional Kakeya sets

Abstract：A Kakeya set is a set of points in Euclidean space which contains a unit line segment in every direction. The Kakeya conjecture asserts that every Kakeya set in n-dimensional space has Hausdorff dimension n. The planar case was proved by Davies in 1971, the finite-field analogue by Dvir in 2008, and the three-dimensional case by Wang and Zahl in 2025. In this talk, we focus on Besicovitch’s classical construction of a planar Kakeya set with zero Lebesgue measure. We will explain the geometric ideas behind the construction and show how a set of area zero can nevertheless contain a unit segment in every direction. The only prerequisite for this talk is basic mathematical analysis.

（文：申爽/审核：郭千桥）