Triangle Inequality

What is the triangle inequality good for in math? When do we use it? Why do we use it?

 

The triangle inequality theorem is one of the important mathematical principles that is used across various branches of mathematics. In real life, civil engineers use the triangle inequality theorem since their area of work deals with surveying, transportation, and urban planning. The triangle inequality theorem helps them to calculate the unknown lengths and have a rough estimate of various dimensions.

The Triangle Inequality Theorem says:

Any side of a triangle must be shorter than the other two sides added together.
If it is longer, the other two sides won't meet!
If a side is equal to the other two sides it is not a triangle (just a straight line back and forth).

According to the Triangle Inequality theorem:

AB + BC must be greater than AC, or AB + BC > AC.
AB + AC must be greater than BC, or AB + AC > BC
BC + AC must be greater than AB, or BC + AC > AB.


The triangle inequality is useful in mathematical analysis for determining the best upper estimate on the size of the sum of two numbers, in terms of the sizes of the individual numbers. if and only if one of the vectors x or y is a nonnegative scalar of the other.

 

You said:

"If a side is equal to the other two sides it is not a triangle. . ."

Is this not the definition of an equilateral triangle?

 

by the definition, in an equilateral triangle "all sides are equal"

but in case, if one side (a) is equal to the sum other two sides (b+c), it is not a triangle

 

Of course, you are talking about Euclidean Geometry. This doesn't apply to non-Euclidean Geometries.

 

Yes, it does apply to non-Euclidean geometries!

 

How would I ever know that? Do you think I am planning to explore advanced geometries? I am happy just to review high school geometry.

 

Well, then, why did you make an assertion about non-Euclidean geometry?

 

What do I know, right? I am a math person
WANT-TO-BE, RIGHT?