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# 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 a^{2}+b^{2} = c^{2}, and a = b and c = 6, then we get 2a^{2} = 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 6^{2}+6^{2} = c^{2}, and solving for c, we get c = 72^{.5} or c = sqrt(72), which is ~8.49 feet.

Thanks for reading.

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