Difference between revisions of "Triangle Inequality"
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| − | The Triangle Inequality can also be extended to other [[polygon]]s. The lengths <math>a_1, a_2, \ldots, a_n</math> can only be the sides of a nondegenerate <math>n</math>-gon if <math>a_i < a_1 + \ldots + a_{i -1} + a_{i + 1} + \ldots + a_n = \left(\sum_{ | + | The Triangle Inequality can also be extended to other [[polygon]]s. The lengths <math>a_1, a_2, \ldots, a_n</math> can only be the sides of a nondegenerate <math>n</math>-gon if <math>a_i < a_1 + \ldots + a_{i -1} + a_{i + 1} + \ldots + a_n = \left(\sum_{j=1}^n a_j\right) - a_i</math> for <math>i = 1, 2 \ldots, n</math>. |
Revision as of 14:38, 17 August 2006
The Triangle Inequality says that in a nondegenerate triangle 
:
That is, the sum of the lengths of any two sides is larger than the length of the third side. In degenerate triangles, the strict inequality must be replaced by "greater than or equal to."
The Triangle Inequality can also be extended to other polygons. The lengths 
can only be the sides of a nondegenerate 
-gon if 
for 
.
Example Problems
Introductory Problems
See Also
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