SIMPLE POLYGON Meaning and
Definition
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A simple polygon is a geometric figure comprising a closed shape formed by straight line segments, where those segments do not intersect with each other except at their endpoints. This means that there are no self-intersections, crossovers, or overlapping lines within the polygon. In simpler terms, a simple polygon does not have any "holes" or regions of the plane enclosed within its boundaries.
To be considered a simple polygon, certain criteria must be satisfied. Firstly, the polygon must be closed, meaning that the endpoints of the line segments coincide to form a continuous loop. Secondly, none of the line segments should intersect with each other, apart from at their initial and final points. Additionally, the segments must not overlap.
A simple polygon possesses several distinguishing characteristics. It has precisely one interior region (in contrast to complex polygons with multiple enclosed areas) and one exterior region. Moreover, each vertex of the polygon has exactly two neighboring vertices (except for the first and last vertices, which are connected). It is worth noting that a simple polygon can have any number of sides, ranging from three (a triangle) to an infinite number.
Simple polygons are frequently encountered in various fields, including mathematics, computer science, and engineering. They serve as fundamental components in numerous geometric algorithms, simulations, and modeling applications.
Etymology of SIMPLE POLYGON
The word "simple" in "simple polygon" comes from the Latin word "simplus", which means "single" or "simple". The term "simple polygon" refers to a polygon that does not intersect itself, meaning that its edges do not cross each other. The word "polygon" also has a Latin origin, derived from the Greek words "poly", meaning "many", and "gonia", meaning "angle". Hence, "simple polygon" describes a shape with many angles that is single and undivided.
