Original Question
Hilbert's original question was more complicated: given any two tetrahedra T1 and T2 with equal base area and equal height (and therefore equal volume), is it always possible to find a finite number of tetrahedra, so that when these tetrahedra are glued in some way to T1 and also glued to T2, the resulting polyhedra are scissors-congruent?
Dehn's invariant can be used to yield a negative answer also to this stronger question.
Read more about this topic: Hilbert's Third Problem
Famous quotes containing the words original and/or question:
“... in nine out of ten cases the original wish to write is the wish to make oneself felt ... [ellipsis in source] the non-essential writer never gets past that wish.”
—Elizabeth Bowen (1899–1973)
“When performing an autopsy, even the most inveterate spiritualist would have to question where the soul is.”
—Anton Pavlovich Chekhov (1860–1904)