#### Event Title

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#### Document Type

Open Access

#### Faculty Sponsor

Christina Tonnesen-Friedman

#### Department

Mathematics

#### Start Date

21-5-2021 1:00 PM

#### Description

What is the maximum number of people to be allowed in a certain area to practice social distancing during COVID-19? Scientists recommend that people keep at least two meters away from each other, then we can imagine each person to be at the center of a circle of radius one meter, where the circles cannot overlap. Thus, solving the aforementioned social distancing problem amounts to fitting as many non-overlapping equal-sized circles into a confined floor plan as possible. This is the so-called circle packing problem in geometry, which concerns the best (densest) way to arrange non-overlapping circles on a plane. We will calculate the density of square packing as well as hexagon packing of circles, and go over Thue's theorem, which says that hexagon packing is the optimal packing of circles.

Circle Packing and the Math of Social Distancing

What is the maximum number of people to be allowed in a certain area to practice social distancing during COVID-19? Scientists recommend that people keep at least two meters away from each other, then we can imagine each person to be at the center of a circle of radius one meter, where the circles cannot overlap. Thus, solving the aforementioned social distancing problem amounts to fitting as many non-overlapping equal-sized circles into a confined floor plan as possible. This is the so-called circle packing problem in geometry, which concerns the best (densest) way to arrange non-overlapping circles on a plane. We will calculate the density of square packing as well as hexagon packing of circles, and go over Thue's theorem, which says that hexagon packing is the optimal packing of circles.