Triangular Inequalities

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/TriangularInequalities.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TriangularInequalities.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Check

v=Table[Random[Real,{-2,2}],{10000},{3}];

(Abs[#1-#2]<=#3<=#1+#2&@@@Permutations[#])&/@Take[v,30]

Union[Length/@Union/@((Abs[#1-#2]<=#3<=#1+#2&@@@Permutations[#])&/@v)]

(Abs[#1-#2]<=#3<=#1+#2&@@@Permutations[#])&/@{Array[a,3],Array[b,3]}//TraditionalForm