New posts in Triangle Inequality

Minimum of $\left|1-\left(ab+bc+ca\right)\right|+\left|1-abc\right|$

Can any norm be used in a product metric

Sides $\frac{|b - c|}{\sqrt{(b^2 + 1)(c^2 + 1)}}, \frac{|c - a|}{\sqrt{(c^2 + 1)(a^2 + 1)}}, \frac{|a - b|}{\sqrt{(a^2 + 1)(b^2 + 1)}}$ of a triangle.

Show that if $a,b \in \mathbb{R}^n$, then $|||a|| - ||b||| \leqslant ||a+b||$

A problem regarding the in-equality of complex numbers .

For $a$, $b$, $c$ the sides of a triangle, show $ 7(a+b+c)^3-9(a+b+c)\left(a^2+b^2+c^2\right)-108abc\ge0$

Norm squared inequality

General Proof for the triangle inequality