WOLFRAM|DEMONSTRATIONS PROJECT

The Triangle Inequality

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|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|
.