# 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

### Abstract

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.