Polygons

A polygon is a two-dimensional geometric figure that is formed by a finite sequence of straight line segments closed in a loop to form a closed chain or circuit.

Classification of Polygons

Polygons can be classified based on the number of sides and the nature of their angles:

  1. Triangles: Polygons with three sides.
  2. Quadrilaterals: Polygons with four sides.
  3. Pentagons: Polygons with five sides.
  4. Hexagons: Polygons with six sides.
  5. Heptagons: Polygons with seven sides.
  6. Octagons: Polygons with eight sides.
  7. Nonagons: Polygons with nine sides.
  8. Decagons: Polygons with ten sides.

And so on...

They can also be classified based on their angles:

  1. Convex Polygons: A polygon where no line that contains a side of the polygon contains a point in the interior of the polygon.
  2. Concave Polygons: A polygon that is not convex.

Properties of Polygons

  1. Sum of Interior Angles: The sum of the interior angles in a polygon with n sides is (n-2) * 180 degrees.
  2. Regular Polygons: A polygon is regular if all sides and angles are equal. In a regular polygon, each interior angle is equal to [(n-2) * 180°]/n, where n is the number of sides.

Applications

Polygons are fundamental in the field of geometry and are used in various other fields including art, architecture, and computer graphics. In computer graphics, complex shapes are often represented as a mesh of polygons, usually triangles or quadrilaterals.