The Math of Social Distancing is a Lesson in Geometry — Quanta Magazine

My latest column for Quanta Magazine connects the geometry of social distancing, a topic on everyone’s mind right now, with sphere packing, a problem mathematicians have been working on for hundreds of years.

Determining how to safely reopen buildings and public spaces under social distancing is in part an exercise in geometry: If each person must keep six feet away from everyone else, then figuring out how many people can sit in a classroom or a dining room is a question about packing non-overlapping circles into floor plans.

In two dimensions, the sphere packing problem is really the circle packing problem, and the best way to pack circles in the plane is known. But it was only recently that mathematicians settled the question about how to most efficiently pack spheres in dimensions 8 and 24. And there are still many open questions in other dimensions!

You can read the entire article here.