# triangle inequality

## triangle inequality

noun Mathematics.
1.
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.
2.
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.
3.
(for metric spaces) the related theorem that the distance between two points does not exceed the sum of their distances from any third point.

Origin:
1960–65

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Based on the Random House Dictionary, © Random House, Inc. 2013.
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If the triangle inequality holds, you can quickly get a near-optimal solution by finding the minimum spanning tree.
The first advance is an optimization of k-means that uses the triangle inequality to avoid unnecessary distance calculations.
Investigate, justify, and apply the triangle inequality theorem.
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