human population (2021) = 7.9 billion. (but this might be a difficult number to accurately estimate these days because governments are vigorously lying about their COVID-19 deaths for political reasons.)

divide by earth area to get 15.49 people / km^2 = 40.1 people / mile^2. (of course, much of earth's area is ocean, sparsely inhabited, so average density on land is higher.)

64560 m^2 per person, or 16.0 acre. a square 254 meters on a side, or circle with diameter 287 m.

difficult: optimally pack of 7.9 billion points onto the surface of the earth ellipsoid, maximizing the geodesic distance between people.

simplify: assume the earth is flat, so the optimal packing is hexagons. the area of a hexagonal cell as a function of distance between centers is A = d^2 * sqrt(3)/2 .

modeling population growth as exponential, the distance between centers as a function of time is

sqrt((earthsurfacearea / (population*(1+growth)^t)) / (sqrt(3)/2))

earthsurfacearea = 510065555000000

population = 7900000000

population growth = 0.0105 (1.05% per year)

t measured in years after 2021

evaluating at t=0, currently the distance is 273 meters. this "average distance between people" is currently shrinking at a rate of 1.426 meters per year, or 3.90 mm / day, or 1 inch every 6.51 days . this might be a good full-scale live demonstration.

the rate decreases over time because the distance asymptotically approaches 0 (humans packed infinitely densely). in one year, the rate will be 1.419 meter/year.

the world population growth rate is itself currently decreasing.

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