A polygon is referred to as a plane figure whose description is done by a finite number of line segments that are straight that are connected to form a polygonal chain that is closed or a polygonal circuit. The bounding circuit, the solid plane region or the combination of the two can be called a polygon.
A polygonal circuit’s elements are referred to its edges or sometimes referred to as sides, and the meeting point of two edges is what is referred to as a polygon’s corner or vertices. In its singular form it is referred to as a vertex. A solid polygon’s interior is sometimes referred to its body. An n-gon is a term that is used to a polygon that has n number of sides. For example: a rectangle is a 4-gon.
A polygon that does not intersect itself can be said to be a simple polygon. Mathematicians are mostly concerned with the polygonal chains from simple polygons which often define or describes a polygon accordingly. Star polygons as well as self-intersecting polygons may be formed where a polygonal boundary is allowed to cross itself.
A polygon is an example of a 2 dimensional of the more common polytope in any dimension number. Many more polygon’s generalizations exist which are defined for different purposes.
CLASSIFICATION OF POLYGONS.
Polygons can be classified in many different ways. Their bases of classification include:
- Number of sides. This is the primary and the most common base of classification of polygons.
- Convexity and non-convexity. Under this, they can be sub-grouped into:
- Convex. Any line that is drawn through the polygon and meets the boundary twice. As a result of this, all the angles in its interior are less than 1800.
- Non-convex. A line which may be found to meet the boundary more than two times. Equivalently, a line segment exists between two boundary points which passes outside the polygon.
- Concave. These are simple and non-convex. At least one interior angle is greater than 1800.
- Simple. The polygon’s boundary does not cross itself.
- Star-shaped. The entire interior can be seen from one point at least.
- Star polygon. A polygon that intersects itself in a regular way.
- Equality and symmetry.
- Equiangular. All angles are equal. (corner angles).
- Cyclic. All the corners rest on a single circle that is referred to as the circumcircle.
- Tangential. This is where all the sides are a tangent to a circle that is inscribed.
- Equilateral. This is where all the ages have the same length.
- Vertex transitive or isogonal. This is where all corners rest within a similar symmetry orbit.
- Regular. This applies where the polygon is both isotoxal and isogonal. Equivalently, it is both equilateral and cyclic or both equiangular and equilateral. Star polygon is the name given to a non-convex polygon that is regular.
- Miscellaneous. They include:
ANGLES.
The two most common types of angles are the interior and exterior angles.
- Interior angle. Interior angles’ sum for a simple n-gon is given as (n – 2) π radians. It can also be gotten by (n – 2) x 180 degrees.
- Exterior angle. These are supplementary angles to the angles in the interior.
