Wikipedia:Reference desk/Archives/Mathematics/2007 July 21

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July 21

World Population question

If you put all of the people in the world into the state of Virginia, could they all fit? If so, how much space would each person have? 151.199.137.18 01:09, 21 July 2007 (UTC) {email removed as per guidlines)

So, you are asking: If the area of the state of Virginia were divided among the world population, how much space would each person have? See if you can answer that question using information you find in these articles. —Bkell (talk) 02:20, 21 July 2007 (UTC)

Certainly if we are allowed to stack people on top of each other, I imagine everyone could fit. We might need to build walls at the borders of Virginia to keep people from spilling out and make the lower levels of the stacking stable. As to what space each person has, this is kind of a variation on the good ol' Kepler conjecture. For people or even log shaped things of a specified length, we would presumably have to use the hexagonal packing, although a proof does not come to mind. --TehMasterPwnerer 01:47, 22 July 2007 (UTC)

Have you done the math? Why do you think we would need to pack everyone so tightly? —Bkell (talk) 06:07, 22 July 2007 (UTC)

Area of Virginia = 111000 km^2. World population = 6000 000 000. Number of square metres in Virginia = 111 000 * (1000 m/km)^2. Number of square meters per person = 18.5. Which is a square roughly sqrt(18.5 m^2) = 4.3 metres on a side. Everyone could stand in Virginia without touching each other. The world is a big place. Try to reproduce the maths yourself. It's all about the units (m^2, m/km, etc.). 196.2.111.133 11:21, 22 July 2007 (UTC)

Stand on Zanzibar#Explanation of the novel's title Gzuckier 15:56, 23 July 2007 (UTC)

And I think the above figures are assuming that Virginia is perfectly flat. Hills and mountains will probably further increase the actual surface area of Virginia from the calculated amount (ie a hill has more surface area than its flat base.) Dugwiki 16:34, 23 July 2007 (UTC)

Streams, rivers, and lakes will decrease the amount of usable surface area, but with each person getting 18 square meters it shouldn't be too much of a problem. —Bkell (talk) 17:19, 23 July 2007 (UTC)