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Your search for ′What is a triangular inequality′ returned the following results:
a consequence of the Pythagorean theorem
In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although cosines may be proven without these theorems.
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a defining property of norms and measures of distance
The triangle inequality is a defining property of norms and measures of distance.
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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.
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a law of triangles which states that, for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side
Triangle inequality is a law of triangles which states that, for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
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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.
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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):
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In Euclidean geometry for right triangles
In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although cosines may be proven without these theorems.
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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.
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three inequalities that are true simultaneously
The triangle inequality is three inequalities that are true simultaneously.
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a geometric theorem that states that the sum of any two sides of a triangle must be greater than the third side
The triangle inequality theorem is a geometric theorem that states that the sum of any two sides of a triangle must be greater than the third side.
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the assertion that for any real numbers \(c\) and \(d\), we have \[|c+d|
the so-called triangle inequality is the assertion that for any real numbers \(c\) and \(d\), we have \[|c+d| \leq|c|+|d| .\]
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