inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions

In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions.

a defining property of a metric space

The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space.

a defining property of norms and measures of distance

The triangle inequality is a defining property of norms and measures of distance.

a requirement upon distance

In a metric space with metric , the triangle inequality is a requirement upon distance: for all , , in .

a consequence of a consequence for right triangles

Since the Pythagorean theorem only applies to right triangles, the triangle inequality is a consequence of a consequence for right triangles.

the parameters , that hold for every triangle, or for every triangle meeting certain conditions of triangles

In geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain conditions.

a theorem about distances

In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and the triangle inequality is written using vectors and vector lengths (norms):

a mathematical result known as triangle inequality

One way of doing that is by using a mathematical result known as triangle inequality.

part of the definition of a metric

In mathematics, triangle inequality is part of the definition of a metric, and distances in mathematics are synonymous to metrics.

In a metric space M with metric d

In a metric space with metric , the triangle inequality is a requirement upon distance: for all , , in .

three inequalities that are true simultaneously

The triangle inequality is three inequalities that are true simultaneously.

a fundamental concept in geometry

The triangle inequality is a fundamental concept in geometry, and geometry has a number of applications in mathematics and physics.

a relationship between absolute values

When and are real numbers, they can be viewed as vectors in , and the triangle inequality expresses a relationship between absolute values.

One of the most basic laws of geometry

One of the most basic laws of geometry is something called the 'triangle inequality.' ...

This important property of a triangle

This important property of a triangle is known as Triangle inequality.

just a property of absolute values

This is just what's called a triangular inequality; this is just a property of absolute values.

the property that guarantees that d(A, B) ≤ d(A, C) + d(B, C)

Then the triangular inequality is the property that guarantees that d(A, B) ≤ d(A, C) + d(B, C).