Editing Wallace–Bolyai–Gerwien theorem (section)

{{short description|Theorem on polygon dissections}}
[[File:Triangledissection.svg|thumb|right|By the Wallace–Bolyai–Gerwien theorem, a [[square]] can be cut into parts and rearranged into a [[triangle]] of equal area.]]

In [[geometry]], the '''Wallace–Bolyai–Gerwien theorem''',<ref>{{Cite journal |last=Gardner |first=R. J. |date=1985-02-01 |title=A problem of Sallee on equidecomposable convex bodies |url=http://www.ams.org/jourcgi/jour-getitem?pii=S0002-9939-1985-0784187-9 |journal=Proceedings of the American Mathematical Society |language=en |volume=94 |issue=2 |pages=329–332 |doi=10.1090/S0002-9939-1985-0784187-9 |issn=0002-9939 |jstor=2045399|doi-access=free }}</ref> named after [[William Wallace (mathematician)|William Wallace]], [[Farkas Bolyai]] and [[P. Gerwien]], is a theorem related to [[Dissection problem|dissections]] of [[polygon]]s. 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 [[Translation (geometry)|translations]] and [[rotation]]s. The Wallace–Bolyai–Gerwien theorem states that this can be done [[if and only if]] two polygons have the same [[area]].

[[William Wallace (mathematician)|Wallace]] 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.