triangle inequality
Shortcut never longer
The triangle inequality is a principle stating that any side of a triangle must be shorter than the sum of the other two sides.
In mathematics, this extends to distances and measurements generally: the direct path between two points is never longer than any indirect route.
The triangle inequality tells us that |a + b| ≤ |a| + |b|.
- sumAddition's result
- distanceSpace between two points
- boundSecured or destined
- Euclidean geometryStudy of flat planes
- geometric proofsLogical arguments about shapes
proof by contradiction · side · axioms · hypotenuse · similarity · taxicab · congruence · absolute value · spatial reasoning · vertex · norm · constraint · proportionality · detour · theorem · edges · deviation · geometry
- Trianglesequilateral, isosceles, scalene, hypotenuse, vertex
- Geometry TheoremsPythagorean theorem
- functional analysisnorm, norms, completeness, orthogonality, subspaces
- geometryangles, circles, angle, shapes, lines
- Geometry Axiomsbetweenness, incidence