AM–GM inequality
states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list
Facts
6 properties- Instance of
- inequality
- Part of
- HM-GM-AM-QM inequalities[5]
- Defining formula
- H \le G \le A[6]
- Maintained by WikiProject
- WikiProject Mathematics[7]
- Named after
- Augustin-Louis Cauchy, arithmetic mean, geometric mean[2][3][4]
🏷️ Also known as
en inequality of arithmetic and geometric means
en relation between AM GM
en AM–GM inequality
ar متباينة الوسطين الحسابي والهندسي
ar متفاوتة المتوسطين الحسابي و الهندسي
cs AG nerovnost
cs Nerovnost aritmetického a geometrického průměru
cs AG-nerovnost
de geometrisch-arithmetische Ungleichung
de Mittelungleichung
de Ungleichung vom arithmetischen und geometrischen Mittel
de AGM-Ungleichung
de Ungleichung der Mittelwerte
el ανισότητα ΑΜ-ΓΜ
el ανισότητα αριθμητικού-γεωμετρικού μέσου
el ανισότητα AM-GM
es desigualdad de las medias aritmética y geométrica
fa نابرابری میانگین حسابی-هندسی
fa نامساوی میانگین حسابی-هندسی
fa نابرابری تیریث
🔖 Identifiers · 7
- OpenAlex ID
- C20565195
- Image (Wikimedia Commons)
- AM GM inequality visual proof.svg ↗
- Digital Library of Mathematical Functions ID
- 1.7.E7
- Freebase ID
- /m/02vr2n
- MathWorld ID
- CauchysFormula
- PlanetMath ID
- ProofOfArithmeticgeometricMeansInequality, ArithmeticgeometricharmonicMeansInequality, ProofOfArithmeticgeometricharmonicMeansInequality2
- Yle topic ID
- 18-245691
🔗 Connections
Named after 3
Instance of 1
Maintained by WikiProject 1
Part of 1
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Summary
AM–GM inequality is an inequality[1].