The math of social distancing
The social distancing recommendations due to coronavirus pandemic are to keep a minimum 6-feet distance between persons.
Round table
Let us assume you want to sit with a group of ‘n’ friends for a dinner (this is theoretical and not recommended in practice) at a round table. You need to know how big the table should be.
Your sitting arrangement could be described as a regular polygon:
You and your friends will sit at the corners and ‘a’ is the distance between parties. The table radius could be computed as:
For example to sit 5 people you need a table with 5.104 feet or 1.556-meter radius.
Cocktail Party
If you want to go for more informal arrangements and instead of a sit-down dinner you want to get together for standing up cocktail party (also not recommended!). In this case, we need to arrange the group of the people on the floor in the most efficient manner, maintaining the minimal distance.
This is known in math as a circle packing problem. Imagine each person inside an invisible circle with a 3 feet radius. As long as circles do not intersect, that would ensure a 6 feet distance between any two guests.
In 1773 Lagrange proved that the hexagonal packing arrangement provides highest packing density:
The side of the hexagon in the figure above would be our 6 feet minimal distance.
Disclaimer: the post is just an intellectual exercise to keep you entertained while you stay at home weathering out the pandemic. I do not recommend arranging any dinners or cocktail parties at this time.