Linked from

The 13 pages that link to Convexity, each with the reason it gives.

• Triangle inequalityRelated: For Euclidean points, equality occurs when the intermediate point lies on the segment between them.

• Line segmentRelated: Segments provide the defining test for whether a geometric set is convex.

• Chernoff boundRelated: Convexity helps control exponential moments and derive bounds from limited information.

• Equality conditionRelated: Strict convexity often determines whether equality can occur only when compared inputs coincide.

• Geometric inequalityRelated: Convexity often turns geometric structure into sharp bounds on lengths, areas, and averages.

• Mathematical optimizationRelated: Convexity separates problems with dependable global-optimum guarantees from harder cases.

• Platonic solidRelated: Convexity excludes indented polyhedra from the Platonic solids.

• Minkowski inequalityRelated: Convexity underlies norm inequalities and characterizes the relevant range p ≥ 1.

• Euler's polyhedron formulaRelated: Convexity guarantees the polyhedron encloses a sphere-like surface without handles or cavities.

• BetweennessRelated: Convexity is defined through the points lying between pairs of points.

• Levinson's inequalityRelated: The third-derivative condition implies convexity of the first derivative.

• Pasch's theoremRelated: The crossing behavior reflects the convex shape enclosed by a triangle.