Meanings
- geometryThe observation 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 another triangle with area F, then A²(b²+c²-a²)+B²(a²+c²-b²)+C²(a²+b²-c²)≥16Ff,, with equality if and only if the two triangles are similar with pairs of corresponding sides (A, a), (B, b), and (C, c).
Synonyms: Neuberg-Pedoe inequality
Synonyms & antonyms
proper nounThe observation 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 another triangle with area F, then A²(b²+c²-a²)+B²(a²+c²-b²)+C²(a²+b²-c²)≥16Ff,, with equality if and only if the two triangles are similar with pairs of corresponding sides (A, a), (B, b), and (C, c).
Origin
Named after Daniel Pedoe.
Full word history & related roots →Cite this entry
Pedoe's inequality. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Pedoe's%20inequality
“Pedoe's inequality.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Pedoe's%20inequality. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “Pedoe's inequality,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Pedoe's%20inequality.
Source: Pedoe's inequality on Wiktionary, CC BY-SA 4.0.