Wallace–Bolyai–Gerwien theorem

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, the Wallace–Bolyai–Gerwien theorem, named after <a href="/facts/William_Wallace_(mathematician)/KPxrPjQX">William Wallace</a>, <a href="/facts/Farkas_Bolyai/0d7WzLo7">Farkas Bolyai</a> and P. Gerwien, is a theorem related to <a href="/facts/Dissection_problem/lslQIYpS">dissections</a> of <a href="/facts/Polygon/yAq7RjPz">polygons</a>. It answers the question when one polygon can be formed from another by cutting it into a finite number of pieces and recomposing these by <a href="/facts/Translation_(geometry)/KlpWmnfX">translations</a> and <a href="/facts/Rotation/yChkz49x">rotations</a>. The Wallace–Bolyai–Gerwien theorem states that this can be done <a href="/facts/If_and_only_if/bYSxGJ66">if and only if</a> two polygons have the same <a href="/facts/Area/KsNG1G9t">area</a>.
<a href="/facts/William_Wallace_(mathematician)/KPxrPjQX">Wallace</a> had proven the same result already in 1807.
According to other sources, Bolyai and Gerwien had independently proved the theorem in 1833 and 1835, respectively.

Wallace–Bolyai–Gerwien theorem open-in-new

Wallace–Bolyai–Gerwien theorem