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Triangle inequality - Wikipedia

https://en.wikipedia.org/wiki/Triangle_inequality

Triangle inequality · In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or ...

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Triangle inequality | Theorem, Geometry, & Degenerate | Britannica

https://www.britannica.com/science/triangle-inequality

Mar 22, 2024 ... The triangle inequality is the theorem in Euclidean geometry that the sum of any two sides of a triangle is greater than or equal to the ...

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gn.general topology - Why the triangle inequality? - MathOverflow

https://mathoverflow.net/questions/65513/why-the-triangle-inequality

May 20, 2011 ... 6 Answers 6 ... The triangle inequality is natural. ... It was Lawvere who first realized that the above sounds like composition of morphisms in a ...

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Triangle Inequality -- from Wolfram MathWorld

https://mathworld.wolfram.com/TriangleInequality.html

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

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A note on the triangle inequality for the Jaccard distance

https://arxiv.org/abs/1612.02696

Dec 8, 2016 ... Title:A note on the triangle inequality for the Jaccard distance ... Abstract:Two simple proofs of the triangle inequality for the Jaccard ...

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Using the Triangle Inequality to Accelerate k-Means

https://cdn.aaai.org/ICML/2003/ICML03-022.pdf

Many papers have also been published on speeding up ¡ - means or nearest neighbor search using inequalities that are specific for Euclidean distance, for ...

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A Triangle Inequality for Cosine Similarity

https://arxiv.org/abs/2107.04071

Jul 8, 2021 ... Recently, Cosine similarity has become a popular alternative choice to the standard Euclidean metric, in particular in the context of textual ...

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Triangle Inequality

https://sites.math.washington.edu/~king/.../10-03-Triangle-Inequality.html

“Triangle equality” and collinearity. Theorem: If A, B, C are distinct points in the plane, then |CA| = |AB| + |BC| if and only if the 3 points are collinear ...

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Triangle Inequality Theorem- Definition, Formula, Proof, Examples

https://www.cuemath.com/geometry/triangle-inequality-theorem/

The triangle inequality theorem states that, in a triangle, the sum of lengths of any two sides is greater than the length of the third side. Suppose a, b and c ...

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Using the triangle inequality to accelerate k-means | Proceedings of ...

https://dl.acm.org/doi/10.5555/3041838.3041857

Aug 21, 2003 ... The accelerated algorithm avoids unnecessary distance calculations by applying the triangle inequality in two different ways, and by keeping ...

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