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EQUIDISSECTION

Equidissection

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

Monsky's theorem

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

Monsky's_theorem

Zonogon

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

Kite (geometry)

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)

Kite_(geometry)

Dissection problem

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

Dissection_problem

Elaine Kasimatis

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

Elaine_Kasimatis

List of triangle topics

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

List_of_triangle_topics

Affine-regular polygon

{\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

Affine-regular_polygon

Sherman K. Stein

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

Sherman_K._Stein

Spectrum (disambiguation)

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)

Spectrum_(disambiguation)