Editing Hilbert's third problem (section)

==History and motivation==
The formula for the volume of a [[pyramid (geometry)|pyramid]], one-third of the product of base area and height, had been known to [[Euclid]]. Still, all proofs of it involve some form of [[Limit of a sequence|limiting process]] or [[calculus]], notably the [[method of exhaustion]] or, in more modern form, [[Cavalieri's principle]]. Similar formulas in plane geometry can be proven with more elementary means. Gauss regretted this defect in two of his letters to [[Christian Ludwig Gerling]], who proved that two symmetric tetrahedra are [[equidecomposable]].<ref name=":0" />

Gauss's letters were the motivation for Hilbert: is it possible to prove the equality of volume using elementary "cut-and-glue" methods? Because if not, then an elementary proof of Euclid's result is also impossible.