Difference between revisions of "Triangular inequality"
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| − | In a triangle ABC, any side is smaller | + | In a [[triangle]] ABC, any side is smaller than 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 ''' | + | This generalizes in mathematics to the '''trianglar 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> | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Latest revision as of 05:49, September 20, 2016
In a triangle ABC, any side is smaller than 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 trianglar 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>