Duality between Different Triangle Inequalities and Triangle Inequalities with (R, r, s)

Abstract

A very useful method in proving geometric inequalities is the transformation of any triangle inequality

$$ F({f_1}({u_1},{v_1},{w_1}),...,{f_n}({u_n},{v_n},{w_n})) \geqslant 0 $$

(1)

where (u_i, v_i, w_i) (i = 1, ..., n) are sets of triangle elements, into a triangle inequality with (R, r, s).