Polygon definition

Author: Matthew David

Introduction
Polygon

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. In geometry a polygon it can be traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners.

In geometry a polygon  is usually a plane shape  that is bounded by a closed  circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called edges or sides, and the points where two edges meet are the polygon's vertex or corners. A polygon is a 2-dimensional.Polygons is primarily classified by the number of sides.

Characteristics of Polygon

Convexity

Polygons may be characterized by their degree of convexity:

Convex: any line and it can be drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
Non-convex: a line may be found which meets its boundary more than twice.
Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
Concave: Non-convex and simple.
Star-shaped: the whole interior is the visible from and that is a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
Self-intersecting: the boundary of that  polygon crosses itself. Branko Grünbaum calls these Coptic, though this term does not seem to be widely used. The term complex is sometimes that can be used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.
Star polygon: it is a polygon which can be self-intersects in a regular way.

A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc and it can be a different great circle and you have a digon. Regular Polygon Usually two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge. A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees.

Special Nmaesof Polygons

Some polygons have special names and that are depending on the number of sides they have.



Number of sides              Name of polygon

3                            Triangle

4                            Quadrilateral

5                            Pentagon

6                            Hexagon

7                            Heptagon

8                            Octagon

9                            Nonagon

10                           Decagon

Classifying Polygons:

There are two categories of polygon. They are convex and concave. Polygons are also classified by the number of sides they have. The following list shows that the polygon name and number of sides they have.  

Triangle - three-sided polygon.

 Quadrilateral - four-sided polygon.

 Pentagon - five-sided polygon.

 Hexagon - six-sided polygon.

 septagon -seven-sided polygon.

 Octagon - eight-sided polygon.

 Nonagon - nine-sided polygon.

 Decagon - ten-sided polygon

Regular polygon:

A regular polygon is a polygon which has equal angles  and equilateral . Regular polygons may be convex or star.
Regular convex polygons:
1. Introduction to Square:

A square is one of the regular quadrilateral.  it has four equal sides and four equal angles .All angles are 90 degree .The total internal angles of square is 360 degree.

Square
2.Introduction to Equilateral triangle:

An equilateral triangle is one type of polygon.it has three sides.They are equal in length and the total internal angle of triangle is 180 degree.All the three angles are equal.(each 60 degree).

Equilateral triangle

3. Introduction to Pentagon:

The five sided polygon is known as pentagon. The sum of internal angle of a pentagon adds up to 540 degree. The all internal angles are equal( each 108 degree)

Pentagon
4.Introduction to Hexagon:

The six sided polygon is known as hexagon with equal length (regular hexagon).the sum of internal angle of a hexagon adds up to 720 degree. The all internal angles are equal (each 120 degree).

Hexagon

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