Estimation quiz!

[StephenG1CMZ]

The emphasis on efficient packing of circles is an interesting mathematical problem, but all the reports I have seen concentrate exclusively on packing density.

For real world Covid-19 safety, other measurements will also be important: Path length through such a packed park, for example.

Imagine 4 regularly spaced circles. It is easy to walk through the park between the circles (Unless you need an additional circle around your path). Or imagine a fireman trying to reach one of the circles.

Now, consider doing that with tightly-packed hexagons. Your walk through the park is now much longer than the straight path with 4 circles.

Is there any prediction of path length for the various configurations?