Equidecomposability (scissors congruence) of polyhedra in R^3 and R^4 is algorithmically decidable: Hilbert's 3rd Problem revisited
Владик Крейнович · scholarworks - UTEP (The University of Texas at El Paso) · 2008
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 ) are scissors congruent (equidecomposable) i.e., they can be both decomposed into the same nite number of pair-wise congruent polygonal pieces: P = P 1 ∪ . . .∪ P p , P = P 1 ∪ . . .∪ P p , and P i ∼ P i .In one of the 23 problems that D. Hilbert formulated in 1900 as a