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What Is a Polygon OR

# What Is a Polygon

A polygon is a plane figure that consists of a number of straight line segments where the line segment end points are joined to form the outline of the entire figure. A polygon is usually a closed plane curve, meaning that the lines will meet at the same point on itself when moving in one direction and diverge from the same point on itself when moving in the opposite direction.

### Number

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A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges. The point where two line segments meet is called vertex or corners, henceforth an angle is formed. An example of a polygon is a triangle with three sides. A circle is also a plane figure but it is not considered a polygon, because it is a curved shape and does not have sides or angles. Therefore, we can say, all the polygons are 2d shapes but not all the two-dimensional figures are polygons. However many sides a polygon has is the same number of exterior angles it has. So, a pentagon with five sides has five exterior angles. A hexagon will have six exterior angles and so on. For regular polygons, we can figure out the measurement of the exterior angle, but for polygons that aren't regular, we can't. Here is the formula for regular polygons:

Exterior angle – The exterior angle is the supplementary angle to the interior angle. Tracing around a convex n-gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full turn, so the sum of the exterior angles must be 360°. This argument can be generalized to concave simple polygons, if external angles that turn in the opposite direction are subtracted from the total turned. Tracing around an n-gon in general, the sum of the exterior angles (the total amount one rotates at the vertices) can be any integer multiple d of 360°, e.g. 720° for a pentagram and 0° for an angular "eight" or antiparallelogram, where d is the density or turning number of the polygon. See also orbit (dynamics). The word polygon comes from Late Latin polygÅnum (a noun), from Greek πολÏγωνον (polygÅnon/polugÅnon), noun use of neuter of πολÏγωνος (polygÅnos/polugÅnos, the masculine adjective), meaning "many-angled". Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions. (Source: en.wikipedia.org)

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