Category:Examples of Triangle Inequality
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This category contains examples of use of Triangle Inequality.
Geometry
Given a triangle $ABC$, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.
In the words of Euclid:
(The Elements: Book $\text{I}$: Proposition $20$)
Real Numbers
Let $x, y \in \R$ be real numbers.
Let $\size x$ denote the absolute value of $x$.
Then:
- $\size {x + y} \le \size x + \size y$
Complex Numbers
Let $z_1, z_2 \in \C$ be complex numbers.
Let $\cmod z$ denote the modulus of $z$.
Then:
- $\cmod {z_1 + z_2} \le \cmod {z_1} + \cmod {z_2}$
Pages in category "Examples of Triangle Inequality"
The following 6 pages are in this category, out of 6 total.