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Extended data to n=100.
Joseph O'Rourke
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Some empirical data, with each point the average of 50 trials:
           MinDistSquare http://cs.smith.edu/~orourke/MathOverflow/MinDistSquare.jpg
The curve $1/(\sqrt{2} n)$ fits rather well. Congrats to Douglas Zare and Ori Gurel-Gurevich!

Joseph O'Rourke
  • 150.8k
  • 36
  • 358
  • 958