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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
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
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
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)
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
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
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
{\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
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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Surname or Lastname
English (Cumbria)
English (Cumbria) : variant of Irvin.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
The Plaids; Name of a Star
Surname or Lastname
English
English : variant of Kenyon.
Boy/Male
English
Surname used as a given name.
Female
English
Variant spelling of English Dixie, DIXEE means "tenth."
Boy/Male
Indian
Light of Win
Girl/Female
Muslim
Study, Read (Celebrity Name: Sanjay Dutt)
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Poetess
Boy/Male
Hindu
Deep water
Female
English
English byname transferred to forename use, BLONDIE means "blonde."
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