Triangle inequality
Property of geometry, also used to generalize the notion of "distance" in metric spaces
Triangle inequality
In mathematics, the triangle inequality states that for any triangle in Euclidean space, the sum of the lengths of any two sides must be greater than or equal to the length of the third side. If a, b, and c are the lengths of the sides of a triangle then: c ≤ a + b . {\displaystyle c\leq a+b.} The same inequality holds when the sides of the triangle are relabeled, so also b ≤ a + c {\displaystyle b\leq a+c} and a ≤ b + c {\displaystyle a\leq b+c} . When one side length is equal to the sum of the other two, c = a + b {\displaystyle c=a+b} , the triangle is degenerate, with zero area. The triangle inequality implies a related statement for Euclidean vectors, also called the triangle...
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