Difference between revisions of "Triangular inequality"
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| − | 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''. | + | 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 ''' | + | 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]] | ||
Revision as of 17:17, June 27, 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 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>