polygon

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Figure 2: The points of a plane that are not on a polygon are separated by the polygon into two regions, the “inside” and the “outside.”

Figure 1: A polygon whose vertices are lattice points.

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Science & Tech

polygon

mathematics

Written and fact-checked by The Editors of Encyclopaedia Britannica

Last Updated: Apr 5, 2024 • Article History

Category: Science & Tech

Key People:: Carl Friedrich Gauss

Related Topics:: hexagon; Pascal’s triangle; flexagon; triangle; regular polygon

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polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides).

If none of the sides, when extended, intersects the polygon, it is a convex polygon. Otherwise, it is concave.

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.

Britannica Quiz

Define It: Math Terms

A polygon with all sides equal is equilateral; an example is a rhombus, which is an equilateral quadrilateral. A polygon with all interior angles equal is equiangular; an example is a rectangle, which is an equiangular quadrilateral. Any polygon that is both equilateral and equiangular is a regular polygon; examples are an equilateral triangle and a square.

The Editors of Encyclopaedia Britannica This article was most recently revised and updated by J.E. Luebering.