Equidissection Equidissection 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 theorem, which states that a square cannot be equidissected into an odd number of triangles. In fact, most polygons cannot be equidissected at all. Much of the literature is aimed at generalizing Monsky's theorem to broader classes of polygons. The general question is: Which polygons can be equidissected into how many pieces? Particular attention has been given to trapezoids, kites, regular polygons, centrally symmetric polygons, polyominos, and hypercubes. Equidissections do not have many
Computational geometry main branches of computational geometry are: The primary goal of research in combinatorial computational geometry is to develop efficient algorithms and data structures for solving problems stated in terms of basic geometrical objects: points, line segments, polygons, polyhedra, etc. Some of these problems seem so simple that they were not regarded as problems at all until the advent of computers. Consider, for example, the "Closest pair problem": One could compute the distances between all the pairs of points, of which there are "n(n-1)/2", then pick the pair with the smallest distance. This brute-force algorithm takes O("n") time; i.e. its execution