Klara Wigzell: Hilbert's Third Problem
Time: Tue 2020-12-08 09.00 - 10.00
Location: Zoom, meeting ID: 672 5020 4655
Lecturer: Klara Wigzell
This essay shows and proves a solution to Hilbert’s Third problem concerning the possible equivalence between volume, equidecomposability and equicomplementability of polyhedra in three-dimensional space.
First, the equivalency between area, equidecomposability and equicomplementability of polygons in the plane is proven through the Wallace-Bolyai-Gerwien Theorem.
Proceeding into three-dimensional space, The Cone Lemma, The Pearl Lemma and Bricard’s Condition are presented and proven.
Lastly, three examples of tetrahedra are displayed, which offer a counterexample to the proposition of equivalency of volume and equidecomposability of polygons in three-dimensional space.