@misc{10481/71646,
year = {2021},
month = {11},
url = {http://hdl.handle.net/10481/71646},
abstract = {Hilbert’s Third problem questioned whether, given two
polyhedrons with the same volume, it is possible to decompose the
first one into a finite number of polyhedral parts that can be put together
to yield the second one. This finite equidecomposition process
had already been shown to be possible between polygons of the same
area. Dehn solved the problem by showing that a regular tetrahedron
and a cube with equal volume were not equidecomposable. In this
paper, we present an infinite fractal process that allows the cube to
be visually reconstructed from a tetrahedron with equal volume. We
have proved that, given two tetrahedrons with the same volume, the
first one can be decomposed into an infinite number of polyhedral parts
that can be put together to yield the second one. This process makes it
possible to obtain the volume of a tetrahedron from the volume of the
parallelepiped, without the use of formulas or the Cavallieri Principle},
keywords = {Hilbert Problem},
keywords = {finite equidecomposition},
keywords = {tetrahedron},
keywords = {fractal},
title = {Note for the Third Hilbert Problem: a Fractal Construction},
author = {Flores Martínez, Pablo and Ramírez Uclés, Rafael},
}