What Is a Polygon?
A polygon is a flat, two-dimensional (2D) closed shape made up of three or more straight line segments that are connected end-to-end. The word 'polygon' comes from the Greek words 'poly' (meaning 'many') and 'gonia' (meaning 'angle').
Section 2: Key Characteristics of a Polygon
For a shape to be a polygon, it must meet three key criteria. First, it must be a closed figure, meaning there are no gaps in its boundary. Second, it must be formed by straight line segments, called sides. Third, the sides must not cross over each other (in what is known as a simple polygon). The points where the sides meet are called vertices.
Section 3: A Practical Example
Common examples of polygons are all around us. A triangle is a polygon with three sides. A square, a rectangle, and a diamond are all types of quadrilaterals, which are polygons with four sides. Other examples include a pentagon (5 sides) and a hexagon (6 sides). A circle is a common shape that is not a polygon because its boundary is a curve, not straight line segments.
Section 4: Why Are Polygons Important?
Polygons are a fundamental concept in geometry and are the building blocks for more complex shapes and solids. They are essential in many fields, including architecture for designing buildings and floor plans, art for creating patterns, and computer graphics for generating 2D and 3D images and models in video games and simulations.