Wallace–Bolyai–Gerwien theorem

The set of Bolyai Gerwien is a set of geometry. He states that planar polygons of equal area many congruent triangles can be decomposed into finite.

The set is sometimes called the set of Wallace -Bolyai Gerwien. The Hungarian mathematician Farkas Bolyai and Paul Gerwien (then a lieutenant in a Prussian infantry regiment ) proved the theorem, Gerwien in 1833. Wolfgang Bolyai published his investigations 1832/33 and also sought to take the case any curvilinear surfaces. The Scottish mathematician William Wallace is said to have found the solution earlier ( 1807).

Generalizations

The analogous statement for three - and higher-dimensional polyhedra is not true. Polyhedra of equal volume with different Dehn invariants can not be decomposed into congruent simplices.

Others

It was the end of the 19th century, a mathematical toy which led the decomposition of a square into a triangle equal area according to the theorem in mind.