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 the end, for congenial sympathy, for poetry, for work, for original feeling and expression, for perfect companionship with one’s friends—give me the country.”
—D.H. (David Herbert)
“Everywhere, the ethical predicament of our time imposes itself with an urgency which suggests that even the question “Have we anything to eat?” will be answered not in material but in ethical terms.”
—Hugo Ball (1886–1927)