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5 votes
0 answers
184 views

Question about $n$ random points in a regular polygon, and a limiting probability

Suppose we choose $n$ uniformly random points in a disk, then draw the smallest circle that encloses all of those points. There is evidence suggesting that the probability that the enclosing circle is ...
Dan's user avatar
  • 3,527
13 votes
1 answer
921 views

Limiting shape for Brillouin zones

Is it true that the limiting shape for Brillouin zones (for any lattice) is a circle? You can find the definition and the step by step construction of Brillouin zones here. This picture is taken from ...
Alexey Ustinov's user avatar
20 votes
2 answers
25k views

Partitioning a polygon into convex parts

I'm looking for an algorithm to partition any simple closed polygon into convex sub-polygons--preferably as few as possible. I know almost nothing about this subject, so I've been searching on Google ...
user14059's user avatar
  • 201