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Polygon - Monomath Math Dictionary
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Polygon

Geometry

📖 Definition

A polygon is a closed 2D shape made of straight line segments connected end to end.

📝 Detailed Explanation

Polygons are classified by the number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10), etc. A regular polygon has all sides and angles equal. The sum of interior angles = (n-2) × 180°, where n is the number of sides. Polygons are fundamental in geometry, computer graphics, tiling, and structural engineering.

📐 Formula

Sum of interior angles = (n - 2) × 180°  |  Each interior angle of regular n-gon = (n-2)×180°/n

📜 History & Origins

Polygons have been studied since ancient Greece. Euclid classified polygons in his "Elements." The naming convention uses Greek prefixes (penta = 5, hexa = 6, etc.). Regular polygons are central to the study of geometry and were important in ancient Greek mathematics. The construction of regular polygons with compass and straightedge was a major problem for centuries.

🔗 Related Terms

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