The Math of Social Distancing Is a Lesson in Geometry By Patrick Honner

By Patrick Honner, Contributing Columnist at Quantamagizne

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematician have been studying for centuries

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.uries.

Of course there’s a lot more to confronting COVID than just this geometry problem. But circle and sphere packing plays a part, just as it does in modeling crystal structures in chemistry and abstract message spaces in information theory. It’s a simple-sounding problem that’s occupied some of history’s greatest mathematicians, and exciting research is still happening today, particularly in higher dimensions. For example, mathematicians recently proved the best way to pack spheres into 8- and 24-dimensional space — a technique essential for optimizing the error-correcting codes used in cell phones or for communication with space probes. So let’s take a look at some of the surprising complications that arise when we try to pack space with our simplest shape.

Read the full story at https://www.quantamagazine.org/the-math-of-social-distancing-is-a-lesson-in-geometry-20200713/

Patrick Honner teaches mathematics and computer science in New York City. He is a National STEM Teacher Ambassador, a Math for America master teacher and a recipient of the 2013 Presidential Award for Excellence in Mathematics and Science Teaching. He is a frequent writer, speaker and presenter on mathematics and teaching.