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An example of a convex polygon: a regular pentagon.. In geometry, a convex polygon is a polygon that is the boundary of a convex set.This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon.
The sum of the squared distances from the vertices of a regular n-gon to any point on its circumcircle equals 2nR 2 where R is the circumradius. [4]: p.73 The sum of the squared distances from the midpoints of the sides of a regular n-gon to any point on the circumcircle is 2nR 2 − 1 / 4 ns 2, where s is the side length and R is the ...
It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding diagonals from one vertex to all other non-nearest neighbor vertices. The total number of ways to triangulate a convex n-gon by non-intersecting diagonals is the (n−2)nd Catalan number, which equals (+)...
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.
The strictly convex curves again have many equivalent definitions. They are the convex curves that do not contain any line segments. [21] They are the curves for which every intersection of the curve with a line consists of at most two points. [20] They are the curves that can be formed as a connected subset of the boundary of a strictly convex ...
The convex hull of a simple polygon can also be found in linear time, faster than algorithms for finding convex hulls of points that have not been connected into a polygon. [6] Constructing a triangulation of a simple polygon can also be performed in linear time, although the algorithm is complicated.
Convex polytope - an n-dimensional polytope which is also a convex set in the Euclidean n-dimensional space. Convex set - a set in Euclidean space in which contains every segment between every two of its points. Convexity (finance) - refers to non-linearities in a financial model. When the price of an underlying variable changes, the price of ...