KnowraNesbitt's inequalityLinked fromLinked fromThe 6 pages that link to Nesbitt's inequality, each with the reason it gives.All 6Broader topic 1Related 4Compared with 1AM–GM inequalityRelated: AM–GM supplies a standard lower-bound step in proofs of this inequality.Schur's inequalityRelated: It is a standard three-variable inequality whose proof can use polynomial inequalities related to Schur.Muirhead's inequalityRelated: Homogenization lets Muirhead-style comparisons help establish this classical three-variable inequality.Titu's lemmaBroader topic: Titu's lemma proves this by bounding the sum below using the total numerator and denominator.Shapiro inequalityRelated: Its three-variable case is the first instance of Shapiro’s cyclic bound.Erdős–Mordell inequalityCompared with: This classical inequality has an algebraic reciprocal structure absent from the geometric bound.