The Kakeya Needle Problem
主 题: The Kakeya Needle Problem
报告人: Dr Allison Tanguay, Assistant Professor, (Carleton College，Minnesotta)
时 间: 2015-12-18 13:00 - 14:00
地 点: 理科一号楼 1114
In 1917 S. Kakeya posed "the needle problem," asking: what is the area of the smallest figure in the plane in which a unit line segment (a "needle") can be rotated 180 degrees? It was conjectured that the smallest such "Kakeya set" was a deltoid with area pi/8. However, in 1928 A.S. Besicovitch published a surprising result: Kakeya sets can be made arbitrarily small. More than just a historical and geometrical curiosity, Kakeya sets have come to play an important role in analysis today. In this talk, we will construct a Kakeya set with arbitrarily small area and then discuss some problems that are unexpectedly related to these sets.