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Partition of a polygon into triangles of equal area
In geometry, an equidissection is a partition of a polygon into triangles of equal area. The study of equidissections began in the late 1960s with Monsky's
Equidissection
Convex polygon with pairs of equal, parallel sides
Monsky's theorem, Paul Monsky (1990) proved that no zonogon has an equidissection into an odd number of equal-area triangles. In an n {\displaystyle n}
Zonogon
One can't dissect a square into an odd number of triangles of equal area
triangles of equal area. In other words, a square does not have an odd equidissection. The problem was posed by Fred Richman in the American Mathematical
Monsky's_theorem
Geometric problems involving the partition of a figure
any dimension). A partition into triangles of equal area is called an equidissection. Most polygons cannot be equidissected, and those that can often have
Dissection_problem
Quadrilateral symmetric across a diagonal
each other under this duality are compared in the table below. The equidissection problem concerns the subdivision of polygons into triangles that all
Kite_(geometry)
American mathematician
work on equidissection, the subdivision of polygons into triangles of equal area; with Stein, she made the first studies of equidissections of regular
Elaine_Kasimatis
{\displaystyle m} is even, by affine invariance of equidissection and Monsky's theorem on equidissections of squares. More generally an n {\displaystyle n}
Affine-regular_polygon
of Triangle Centers Equal incircles theorem Equal parallelians point Equidissection Equilateral triangle Euler's line Euler's theorem in geometry Erdős–Mordell
List_of_triangle_topics
American mathematician
independent discoverers of Fáry's theorem, and for his contributions to equidissection, the partition of polygons into triangles of equal area. Stein won the
Sherman_K._Stein
Topics referred to by the same term
Pseudospectrum Spectrum of a polygon, the set of numbers of possible equidissections Spectrum of a sentence, in mathematical logic Spectrum of a theory
Spectrum_(disambiguation)
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