Quote:
Originally Posted by Agemegos
Well the area of a hexagon is ≈0.6495 times the square of the long diagonal, and the long diagonal is 2/sqrt(3) times the width across the flats, so the area of a hex is 0.866 square hexes, and a hex-distance is therefore 0.931 times the square root of the area of a hex, which makes a square-root-area-hex 1.0746 times a centre-to-centre-distance-hex, which means that 1.83 hexes = 1.97 hexes, and don't you wish you had used units of distance and area?
There are eighteen other hexes within two hexes of a hex, and if each has 50% of a star with 14.8% of a habitable planet that means 0.926 chance that each is uninhabitable and 25% chance that they are all uninhabitable. There is 75% of a neighbour at distance one hex or two hexes, which makes it seem to me that an average nearest-neighbour distance of 2.94 or 3.93 hexes seems implausibly large.
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Yeah, I made some interesting choices. But I’m definitely paying attention.
Although, if you have an circle of hexes, r2.5 hexes, that’s 19 hexes, for 9.5 systems, and 1.406 inhabitable planets. Going out to 3.5, that’s 31 hexes, 15 systems, and 2.22 inhabitable planets.
Although that distance is just between easily inhabitable worlds, not all worlds.