The Triangle Inequality
The Triangle Inequality
The triangle inequality is usually expressed algebraically using vectors in two dimensions. This Demonstration shows two vectors, and , and their sum . These three vectors form a triangle unless is a multiple of . The triangle inequality states that the sum of the lengths of two sides of a triangle is at least as large as the length of the third side. In symbols, .
x
y
x+y
x
y
|x|+|y|≥|x+y|