13 Apr
2018
13 Apr
'18
8:50 a.m.
If you dissect a unit disk radially into a large number of equal wedges, it’s well known that you can reassemble them to form a shape that in the limit converges to a 1-by-pi rectangle. What other limiting shapes can we form in the limit from patterns that join the wedges edge-to-edge? I’m guessing that you get a class of curvy pseudoquadrilaterals ABCD where AB is a unit segment, CD is a unit segment, and the curves BC and AD satisfy some sort of curvature-compatibility condition. Jim Propp