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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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Boy/Male
Gaelic
Son of the man from the ford by the oak trees.
Girl/Female
Indian, Sanskrit
The Sovereign Goddess of Life
Male
Egyptian
, a surname of king Rameses III.
Boy/Male
Irish
Little hero.
Girl/Female
Arabic, Muslim
Blessed
Male
Finnish
Pet form of Finnish Aarne, AAKE means "eagle."
Girl/Female
Muslim
Light of contentment
Boy/Male
Tamil
Vishwatma | விஷà¯à®µà®¾à®¤à¯à®®à®¾
Universal soul
Surname or Lastname
English (Devon)
English (Devon) : habitational name from Sweetlands in Upottery, Devon, so named from Old English swēte ‘sweet’, ‘pleasant’, ‘fertile’ + land ‘cultivated land’, ‘estate’, or possibly a topographic name with the same meaning.
Female
Bulgarian
(Радомира), happy peace.
EQUIDISSECTION
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