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In geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a simple polygon is a polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...
that does not intersect
Intersection or intersect may refer to:
* Intersection in mathematics, including:
** Intersection (set theory), the set of elements common to some collection of sets
** Intersection (geometry)
** Intersection theory
* Intersection (road), a pl ...
itself and has no holes. That is, it is a flat shape consisting of straight, non-intersecting line segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between ...
s or "sides" that are joined pairwise to form a single closed path. If the sides intersect then the polygon is not simple. The qualifier "simple" is frequently omitted, with the above definition then being understood to define a polygon in general.
The definition given above ensures the following properties:
* A polygon encloses a region
In geography, regions, otherwise referred to as zones, lands or territories, are areas that are broadly divided by physical characteristics (physical geography), human impact characteristics (human geography), and the interaction of humanity and t ...
(called its interior) which always has a measurable area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while ''surface area'' refers to the area of an open su ...
.
* The line segments that make up a polygon (called sides or edges) meet only at their endpoints, called vertices (singular: vertex) or less formally "corners".
* Exactly two edges meet at each vertex.
* The number of edges always equals the number of vertices.
Two edges meeting at a corner are usually required to form an angle
In Euclidean geometry, an angle is the figure formed by two