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2 unusual facts about Pedoe's inequality


Pedoe's inequality

"A Two-Triangle Inequality", Daniel Pedoe, The American Mathematical Monthly, volume 70, number 9, page 1012, November, 1963.

In geometry, Pedoe's inequality, named after Daniel Pedoe, states that if a, b, and c are the lengths of the sides of a triangle with area ƒ, and A, B, and C are the lengths of the sides of a triangle with area F, then


Azuma's inequality

In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.

Block design

A fundamental theorem, Fisher's inequality, named after the statistician Ronald Fisher, is that b ≥ v in any 2-design.

Hardy space

For 0 < p ≤ q ≤ ∞, the class Hq is a subset of Hp, and the Hp-norm is increasing with p (it is a consequence of Hölder's inequality that the Lp-norm is increasing for probability measures, i.e. measures with total mass 1).

Jensen's inequality

Tristan Needham (1993) "A Visual Explanation of Jensen's Inequality", American Mathematical Monthly 100(8):768–71.

Johan Frederik Steffensen

Steffensen's inequality and Steffensen's method (an iterative numerical method) are named after him.

Lagrange's identity

Since the right-hand side of the identity is clearly non-negative, it implies Cauchy's inequality in the finite-dimensional real coordinate spacen and its complex counterpart ℂn.

Pinsker's inequality

The inequality in the above form was proved independently by Kullback, Csiszár, and Kemperman.

Properties of polynomial roots

It is possible to determine the bounds of the roots of a polynomial using Samuelson's inequality.

Wirtinger's inequality for functions

: For other inequalities named after Wirtinger, see Wirtinger's inequality.


see also