Let
(1)
Equivalently, for complex numbers
(2)
Geometrically, the right-hand part of the triangle inequality states that the sum of the lengths of any two sides of a triangle is greater
than the length of the remaining side.
A generalization is
(3)
See also Metric Space ,
Ono Inequality ,
p -adic Number,
Strong
Triangle Inequality ,
Triangle ,
Triangle
Inequalities ,
Triangular Inequalities Explore this
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References Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Apostol, T. M. Calculus,
2nd ed., Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. Krantz, S. G. Handbook
of Complex Variables. Referenced
on Wolfram|Alpha Triangle Inequality
Cite this as:
Weisstein, Eric W. "Triangle Inequality."
From MathWorld https://mathworld.wolfram.com/TriangleInequality.html
Subject classifications
and 
be vectors. Then the triangle inequality is given by
and 
,
