triangle inequality
Americannoun
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the theorem that the absolute value of the sum of two quantities is less than or equal to the sum of the absolute values of the quantities.
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the related theorem that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.
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(for metric spaces) the related theorem that the distance between two points does not exceed the sum of their distances from any third point.
Etymology
Origin of triangle inequality
First recorded in 1960–65
Example Sentences
Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.
The triangle inequality is used at a key point of the proof, so we first review this key property of absolute value.
From Textbooks • Mar. 30, 2016
This is known more generally as the triangle inequality.
From Textbooks • Mar. 30, 2016
Verify that the vectors a, b, and a + b, and, respectively, a, b, and a − b satisfy the triangle inequality.
From Textbooks • Mar. 30, 2016
Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023
Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
