Geometric inequalities

Geometric inequalities are mathematical statements that relate measures such as lengths, angles, perimeters, and areas in geometric figures, usually expressing that one quantity is always greater than or less than another.

Important properties

• They often set bounds for lengths, areas, or angles in figures like triangles, quadrilaterals, and circles.

• Many geometric inequalities are universal, meaning they hold for all figures of a certain type (e.g., all triangles).

• They are frequently used to prove that certain configurations are optimal or impossible.