University of Cambridge > > Isaac Newton Institute Seminar Series > Public lecture: Unpackable Shapes and the Reinhardt Problem

Public lecture: Unpackable Shapes and the Reinhardt Problem

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  • UserThomas Hales (University of Pittsburgh)
  • ClockWednesday 23 August 2023, 16:00-17:00
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PMVW01 - 5th International Conference on Packing Problems: Packing and patterns in granular mechanics

Some convex disks are more easily packed than others. Squares, triangles, and parallelograms are highly packable in the plane.  In fact, each of these shapes is perfectly packable in the sense that it tiles the plane. On the other hand, the circle is relatively unpackable.  No matter how arranged, a circle packing fills less than 91 percent of the plane.  The Reinhardt problem is to determine the most unpackable centrally symmetric convex disk.  This problem has an amazingly rich structure.

This talk is part of the Isaac Newton Institute Seminar Series series.

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