[math-fun] square-ball non-dissectability

A square and circular disc of equal area are NOT inter-dissectable (i.e. scissors congruent, finite # pieces). Easy proof: Lemma: The total length of curvature-1 boundary can never decrease as you cut up your disc and move the pieces around (gluing them at common boundary). But it must decrease, in fact to 0, to achieve the conversion. Contradiction.