Buzz
Polygons vary widely in their forms and dimensions. Truly, they do. khalus / Getty ImagesWhether you're preparing for a math exam, assisting your child with their schoolwork, or simply refreshing your knowledge for a trivia competition, grasping the essentials of polygons will prove highly advantageous.
What Are Polygons?
Polygons are two-dimensional shapes composed of straight lines that connect to form a closed figure with a single boundary. The term "polygon" originates from two ancient Greek words: "poly," meaning many, and "gon," which refers to angles.
In everyday life, polygon shapes (closed figures with straight sides) can be seen in objects like a regular pentagon-shaped baseball plate or a regular hexagon stop sign. Both regular and irregular polygons are widely used in mathematics and art.
4 Types of Polygons
The name of a polygon is determined by the number of its angles and sides. For instance, the prefix "penta" signifies five, making a five-sided figure a pentagon. This naming convention applies to hexagons, octagons, and others as well.
All polygons can be classified into four main categories. Closed shapes with more than three sides and angles are categorized as convex, concave, regular, or irregular polygons.
1. Regular Polygon
A regular (or simple) polygon features equal angles and sides of identical length. These polygons are also classified as convex because their equal sides curve inward at the connection points, forming multiple v-shaped vertices.
2. Irregular Polygon
An irregular (or complex) polygon has at least one interior angle that differs from the others. This irregularity arises from sides of unequal lengths, stretching the shape and creating non-consecutive vertices where diagonals intersect.
3. Convex Polygon
All convex polygons are part of the regular polygon family. However, the convex classification emphasizes the interior angles. For an n-sided polygon to be convex, every interior angle must measure 180 degrees or less.
4. Concave Polygon
Concave polygons feature at least one corner or exterior angle that points inward within the shape's boundary. This inward curve can result in sharp exterior angles, sides of varying lengths, and at least one interior angle exceeding 180 degrees.
4 Rules For Regular Polygons
Now that you understand how polygons are classified, you can explore the finer details of these shapes. Below are key criteria that every regular polygon with n sides must satisfy.
1. A Polygon Has at Least Three Sides
For a shape to qualify as a polygon, it must have at least three sides and an equal number of angles. An equilateral triangle, with its three equal sides and angles, meets the minimum requirements to be classified as a regular polygon.
2. All the Sides Are the Same Length
Regular polygons can consist of countless straight line segments, but each segment must be of equal length. While a square is the most familiar example, an isosceles triangle can also qualify as regular if its two equal sides match the length of the base.
3. All Interior Angles Are Equal
A polygon is regular only if all its interior angles are identical. To determine each angle, divide 360 degrees by the number of sides the polygon has.
4. Every Interior Angle Must Be Convex
In a regular polygon, all interior angles must be convex. This ensures that no interior angle exceeds 180 degrees, and all sides connect at v-shaped vertices.
While many recognize the infinity symbol, few are aware of its formal name. The horizontal figure-eight is known as a lemniscate, a concept introduced by the Greek philosopher and mathematician Proclus in the fifth century C.E.
