Difference between revisions of "Pythagorean Inequality"

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* [[Triangle]]
 
* [[Triangle]]
 
* [[Law of Sines]]
 
* [[Law of Sines]]
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* [[Law of Cosines]]
  
 
[[Category:Inequality]]
 
[[Category:Inequality]]
 
[[Category:Geometry]]
 
[[Category:Geometry]]
 
[[Category:Theorems]]
 
[[Category:Theorems]]

Revision as of 19:03, 1 July 2017

The Pythagorean Inequality is a generalization of the Pythagorean Theorem, which states that in a right triangle with sides of length $a \leq b \leq c$ we have $a^2 + b^2 = c^2$. This Inequality extends this to obtuse and acute triangles. The inequality says:

For an acute triangle with sides of length $a \leq b \leq c$, $a^2+b^2>c^2$. For an obtuse triangle with sides $a \leq b \leq c$, $a^2+b^2<c^2$.

This inequality is a direct result of the Law of Cosines, although it is also possible to prove without using trigonometry.

See also

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