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.
If we're packing circles, don't we need to take into account that the 6ft distance is to the next person -- that is the centre of the next circle, rather than the boundary of it?<p>That means circles of radius 3ft, for a total of 8,693 square miles.
This only works if the target country is a circle itself. The packing method becomes much more difficult when you have to deal with arbitrarily complex shapes. We run into this type of problem in windfarm planning.<p>You have a ridge with discontinuous bands of acceptably sloped terrain, usually highly irregular shapes and you have to fit wind turbines along it, taking into account the minimum clearance between turbines and pack as many as possible within. This type of problem is NP-Hard and almost always ends up being done manually due to additional constraints. These include, access road placement, viewsheds, and turbulence modelling.
You can fit all the humans on earth into a 1km cube.<p>Average volume of a human is 66l [1]. Make it 130l to allow some unused space due to imperfect packing.<p>7.6 billion * 130l = 988 000 000 000 liters.<p>1 cubic kilometer = 1 000 000 000 000 liters.<p>[1] <a href="https://www.wolframalpha.com/input/?i=average%20volume%20of%20human%20body" rel="nofollow">https://www.wolframalpha.com/input/?i=average%20volume%20of%...</a>
As a more practical usecase, how many other EEs have leveraged circles-in-a-circle packing tables such as [1] to approximate cable diameter and/or size conduit?<p>Would be interesting to learn how other disciplines have applied such a tool to solve real-world problems.<p>[1] <a href="http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html" rel="nofollow">http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html</a>
This seems to be a dramatic simplification, to the point where the results aren't helpful at all, unless I'm missing something.<p>A lot of this is private property. Offices, people's houses, a farmer's farmland. We can't go inside, or trample on the crops of farmers. Then you need to subtract roads - because you can't walk on a road and definitely not a motorway.<p>So really, shouldn't the land area used be the <i>publicly accessible pedestrian area</i>?<p>And I dunno about others, but my footpaths are less than a metre long in width in my residential area. In the commercial areas, they tend to be less than 6 metres.
Things are pretty tight in Singapore, I wonder if you take into account places not safe to stand like roads and places occupied by walls, trees, bank vaults etc., if it would be impossible. Almost 6 million people in 7.8 billion square feet if it was just flat land = approx 1300 square feet per person if my math is right.
So, my country which feels big to me couldn't do it.
This reinforces my belief that there are way too many of our species on this planet. Given that 2.1 or so is the replacement rate, a "hard" limit of two child per woman would be decent compromise as this would equate to somewhere around 1.7 taking into account women who don't want to /can't have children. In one generation, if there were no unintended consequences this would drop the population by 15%.<p>Sometime in the 2100s it would be half what it is today and my country could easily fit everyone!