semiopedia.org
Polygons

Polygons

Polygons are closed geometric figures consisting of straight line segments connected end-to-end to form a closed shape.

Polygons

A polygon is a fundamental geometric shape composed of straight line segments (called edges or sides) that are connected end-to-end to form a closed figure. The word "polygon" derives from Greek, where "poly" means "many" and "gon" means "angle."

Basic Properties

Every polygon has these essential characteristics:

  • Sides: Straight line segments that form the boundary
  • Vertices: Points where two sides meet
  • Interior angles: Angles formed inside the polygon at each vertex
  • Perimeter: The sum of all side lengths
  • Area: The space enclosed by the polygon

Classification

By Number of Sides

  • Triangle (3 sides)
  • Square (4 sides)
  • Pentagon (5 sides)
  • Hexagon (6 sides)
  • Octagon (8 sides)
  • Decagon (10 sides)

By Regularity

  • Regular polygons: All sides and angles are equal
  • Irregular polygons: Sides or angles may differ

By Convexity

  • Convex: All interior angles are less than 180°
  • Concave: At least one interior angle exceeds 180°

Applications

Polygons have numerous practical applications across various fields:

  1. Architecture
  1. Nature
  1. Technology
  • Computer graphics and 3D Modeling
  • Game design
  • Digital art creation
  1. Art and Design

Mathematical Properties

Interior Angle Sum

For any polygon with n sides:

  • Interior angle sum = (n-2) × 180°
  • Each interior angle in a regular polygon = ((n-2) × 180°)/n

Area Calculation

Various methods exist for calculating polygon areas:

Notable Relationships

Polygons form the basis for many advanced geometric concepts:

Historical Significance

Throughout history, polygons have played crucial roles in:

  • Ancient architecture and construction
  • Navigation and celestial navigation
  • Religious and cultural symbolism
  • Development of Mathematical Proof understanding

See Also