セミナー・シンポジウム Seminars & Symposium

【12/16】第7回AIMRジョイントセミナー

2016年度 第7回AIMRジョイントセミナーのご案内

Title

Kelvin’s Conjecture and Experiments of Soap Films

Speaker

奈良 知惠 研究推進員
（明治大学先端数理科学インスティテュート）

Date

2016年12月16日（金） 14:30-15:30

Venue

AIMR本館2階 セミナー室

Abstract

How can space be divided into cells of equal volume so as to minimize the (average) surface area of the boundary? In 1887, Lord Kelvin (William Thomson) conjectured that the partition made by a packing of congruent copies of the truncated octahedron with slightly curved faces is the solution (see Figure 1). His conjecture is based on the rules of Plateau (1873) in the theory of foams (see Figure 2). In1994, Denis Weaire, an Irish physicist, and Robert Phelan showed a counterexample to Kelvin’s conjecture, in which packing consists of two kinds of cells with curved faces.
If we restrict cells to space-fillers, congruent polyhedral tiles, we get the orthic version of Kelvin’s conjecture; the truncated octahedron has the minimum surface area among all polyhedral space-fillers. This conjecture is still open. In this paper we introduce the notion of doubly-covered polyhedra and their unfoldings, which leads to an approach for a partial solution of the new Kelvin’s conjecture.

 

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