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The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper [ 1 ] though it seems that the special case, in which the map is defined for pentagons only, goes ...
If K is a field (such as the complex numbers), a Puiseux series with coefficients in K is an expression of the form = = + / where is a positive integer and is an integer. In other words, Puiseux series differ from Laurent series in that they allow for fractional exponents of the indeterminate, as long as these fractional exponents have bounded denominator (here n).
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
Elitzur's theorem (quantum field theory, statistical field theory) Envelope theorem (calculus of variations) Equal incircles theorem (Euclidean geometry) Equidistribution theorem (ergodic theory) Equipartition theorem (ergodic theory) Erdős–Anning theorem (discrete geometry) Erdős–Dushnik–Miller theorem ; Erdős–Gallai theorem (graph ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle' [1]) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.
A simple polygon is the boundary of a region of the plane that is called a solid polygon. The interior of a solid polygon is its body, also known as a polygonal region or polygonal area. In contexts where one is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon.
A subdivision rule takes a tiling of the plane by polygons and turns it into a new tiling by subdividing each polygon into smaller polygons. It is finite if there are only finitely many ways that every polygon can subdivide. Each way of subdividing a tile is called a tile type. Each tile type is represented by a label (usually a letter).