Introduction
A polygon is a two-dimensional shape that is formed by connecting straight line segments to create a closed figure. It is a plane figure with three or more sides and angles. Polygons are classified by the number of sides they have, as well as the types of angles and lengths of their sides.
Types of Polygons
- Triangle: A polygon with three sides and three angles.
- Quadrilateral: A polygon with four sides and four angles.
- Pentagon: A polygon with five sides and five angles.
Properties of Polygons
Polygons have various properties that distinguish them from other geometric shapes. Some key properties include:
- Sum of interior angles of a polygon with ‘n’ sides: (n-2) x 180 degrees
- Sum of exterior angles of a polygon with ‘n’ sides: 360 degrees
Examples of Polygons
Some examples of polygons include squares, rectangles, triangles, pentagons, and hexagons. These shapes are commonly used in mathematics, architecture, art, and design.
Case Studies
One famous case study involving polygons is the use of tessellations in Islamic art and architecture. Tessellations are arrangements of shapes that fit together without any gaps or overlaps. In Islamic art, tessellations are used to create intricate geometric patterns that symbolize unity and infinity.
Statistics
A study conducted by mathematicians found that polygons are one of the most common shapes used in architecture and design. From building facades to floor tiles, polygons are prevalent in various structures around the world.
