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# Convex polygon

A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon. 

## Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

## Concave polygon

A simple polygon that is not convex is called concave, non-convex or reentrant.

## Convex hull

In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.

## Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

## Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

## Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

## Fan triangulation

A fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing diagonals to all of the other vertices of the polygon.

## Helly's theorem

Helly's theorem is a basic result in discrete geometry on the intersection of convex sets.

## Homothetic transformation

In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.

## Hyperplane separation theorem

In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space.

## Interior (topology)

In mathematics, specifically in topology, the interior of a subset S of points of a topological space X consists of all points of S that do not belong to the boundary of S. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.

## Internal and external angles

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

## Krein–Milman theorem

In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about convex sets in topological vector spaces.

## Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

## List of self-intersecting polygons

Self-intersecting polygons, crossed polygons, or self-crossing polygons are polygons some of whose edges cross each other.

## Mean width

In geometry, the mean width is a measure of the "size" of a body; see Hadwiger's theorem for more about the available measures of bodies.

## Morgan Kaufmann Publishers

Morgan Kaufmann Publishers is a Burlington, Massachusetts (San Francisco, California until 2008) based publisher specializing in computer science and engineering content.

## Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

## Polygon triangulation

In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, Chapter 3: Polygon Triangulation: pp.45–61.

## Simple polygon

In geometry a simple polygon is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pair-wise to form a closed path.

## Tangential polygon

In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle).

## Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

## Triangle

A triangle is a polygon with three edges and three vertices.

## References

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