Difference between revisions of "Triangular inequality"
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This generalizes in mathematics to the '''triangle inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold: | This generalizes in mathematics to the '''triangle inequality''': in a space where the notion of distance between two points (''d(x,y)'') is defined, the following inequality must hold: | ||
: <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math> | : <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math> | ||
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Revision as of 01:05, April 26, 2009
In a triangle ABC, any side is smaller then the sum of the other two sides. However, if the three points are aligned, then there may be equality, but it's never possible that AC > AB + BC.
This generalizes in mathematics to the triangle inequality: in a space where the notion of distance between two points (d(x,y)) is defined, the following inequality must hold:
- <math>\forall x,y,z, d(x,z) \le d(x,y) + d(y,z)\,</math>