Library/Geometry/Solid geometry/Geometric inequalities

Geometric inequalities

Overview
Important

Geometric inequalities are statements comparing geometric quantities (like lengths, areas, volumes, or angles) using inequality signs (>, <, ≥, ≤). They often show that one measurement is always at least as big or as small as another, regardless of the specific shape, as long as certain conditions are met.

Important properties

  • Geometric inequalities can involve sides, angles, areas, perimeters, or volumes.

  • They often express optimal or extremal properties, such as the minimum perimeter for a given area.

  • Famous examples include the triangle inequality and the isoperimetric inequality.

  • Proofs may use algebraic manipulation, geometric construction, or properties like symmetry.

Deeper topics