12/13/2020 · In mathematics, the triangle inequality 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. This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary g, The triangle inequality is a defining property of norms and measures of distance. This property must be established as a theorem for any function proposed for such purposes for each particular space: for example, spaces such as the real numbers, Euclidean spaces, the L p spaces (p ? 1), and inner product spaces.
10/4/2016 · And that’s why it’s called the triangle inequality. It’s just saying that look, this thing is always going to be less than or equal to– or the length of this thing is always going to be less than or equal to the length .
In mathematics, the triangle inequality 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 . If x, y, and z are the lengths of the sides of the triangle, then the triangle inequality states that. z ? x + y, {displaystyle zleq x+y,}, Start with any triangle in 3 space, or in n space for that matter, and move it down into the xy plane. You can always move the triangle , as a rigid body, without changing the lengths of its sides. So if the triangular inequality holds in the xy plane, it applies to the same triangle floating in 3 space, or n space.
Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange, 6/22/2017 · (this is not the triangle inequality) The equivalent of this in n dimensions is (x1+x2 + … +xn)² ? n(x1²+x2² + … + xn²) This is just a statement of …
