14 Apr
2016
14 Apr
'16
2:15 p.m.
Any polygon in Euclidean plane is scissor-congruent to any other of the same area, and this is accomplishable entirely with straight cuts (no curves ever needed). I think that was first shown by Bolyai. So if you want an example where curved cuts are needed, then you need the two shapes to include at least one with a curved boundary. And then it is trivial. Make shape #1 be a square. Shape #2 is got by cutting square in two via an S-curve, rotate pieces, glue along common straight line. Obviously a curved cut is needed to get from 1 to 2. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)