COVID-19 and Pythagorean Theorem

4/7/20

The following picture was floating around social media during the Coronavirus Disease 2019 (COVID-19) pandemic:

While the diagram shows the people along the diagonals are 6 feet apart, a basic application of the Pythagorean Theorem shows the other people are not 6 feet away from each other at all, even though the diagram is implying they are.

If a²+b² = c², and a = b and c = 6, then we get 2a² = 36. Solving for a, the distance between the other people, we get a = 18^.5 or a = sqrt(18), which is 4.24 feet.

Applying the Pythagorean Theorem again, we can answer the question of: what does the diagonal distance need to be so all people are at least 6 feet away from each other? We get 6²+6² = c², and solving for c, we get c = 72^.5 or c = sqrt(72), which is ~8.49 feet.

Thanks for reading.