# Triangle Inequality

The Triangle Inequality is a theorem that simply states that the sum of the lengths of any to sides of a triangle $$a$$ and $$b$$ must be greater than or equal to the final side $$c$$. Formally,

$c \leq a + b$

The above is valid in Euclidean Space but there is a different generalization of the theorem for other types of geometries. The Triangle Inequality in these spaces is a theorem about distances, and it written using vectors and their norms.

$||x + y|| \leq ||x|| + ||y||$

Created: 2022-02-03

Emacs 26.1 (Org mode 9.5)