I may have missed something but shouldn't the radius be 3 feet? With a 6 foot radius, wouldn't everyone be 12 feet apart? The maths is new to me (I was OK up to πr2!) so this might be my mistake.
That means people would only be at least 3 feet away, not 6 feet. The original assumption was right.. need a 6 foot radius, 12 foot diameter to meet social distancing guidelines
It’s a circle-packing model, which means there’s no overlap between the exclusion zones. A radius of 3 feet means you’re at least 3 feet away from the edge of anyone else’s circle. They are at the center of their circle, which is an additional 3 feet away, for a total of 6 feet.
You are not accounting for the fact that next person is not at your circle edge but is inside his own circle, and it is his circle touching yours, not the center of his circle, so 2 persons inside 3 feet radius circles have 6 feet of distance in between.
Your assumption is correct if you overlap circles in a way that everyone is on edge of someone else's circle.
