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
Discrete geometry Discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object. Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital