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Dan
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I like math questions that:

  • can be expressed concisely
  • contain few or no numbers
  • are challenging
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42
Regular polygon of radius $1$ with diagonals: mysterious ring of radius $1/e$?
40
Conjecture: If circular coins of any sizes are in a convex polygonal frame, with each coin touching exactly one edge, then all the coins can move
38
Crazy fact(?) about circles drawn on base of triangle between cevians: they always fit, no matter what their order?
36
Intuition is silent: Find the probability that the smallest circle enclosing $n$ random points on a disk lies completely on the disk, as $n\to\infty$.
34
Conjecture: Given any five points, we can always draw a pair of non-intersecting circles whose diameter endpoints are four of those points.

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