EQUIDECOMPOSABILITY(SCISSORS CONGRUENCE)OF POLYHEDRA IN R3 AND R4 IS ALGORITHMICALLY DECIDABLE:HILBERT'S 3rd PROBLEM REVISITED

摘要

Hilbert's third problem: brief reminder. It is known that in a plane, every two polygons P and P' of equal area A(P) = A(P') arescissors congruent (equidecomposable) — i.e., they can be both de-composed into the same finite number of pair-wise congruent polyg-onal pieces: P = U . U Pp, P' =P_1UUP_p ,andP_i~P_i'.