The Triangle Inequality

|x| + |y| = 3.61 + 2.24 = 5.84

|x + y| = 5.66

The triangle inequality is usually expressed algebraically using vectors in two dimensions. This Demonstration shows two vectors,

x

and

y

, and their sum

x+y

. These three vectors form a triangle unless

x

is a multiple of

y

. 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|

.