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I am attempting to do statistical distribution of a variable number of random points on a flat plane. Context, it's for 2d mapping a star chart for a roleplaying game, and I would like to provide a formula that is good enough without using calculus. I know from GURPS Space 4th edition, that on a 3d map, given volume V and systems N randomly distributed throughout the volume, that the average distance between neighbors will $1.12*\sqrt[3]{\frac VN}$, but so far I have found nothing that doesn't use calculus for the 2-dimensional version other than maybe $\sqrt(\frac AN)$, or $\frac AN$, which seems... too simple?

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