Beauty is truth: geometric inequalities

Extract

The publication of [1], which contains all, or almost all, relevant results from all over the world since Euclid’s time up to the middle 1960s, confirmed that this field of study has good traditions, is alive and in good shape. Two decades have passed and the appearance of [2] proved that this part of mathematics is flourishing more than ever. This field (which we will call GI) is a peculiar one: firstly because the subject matter doesn’t presuppose any great mathematical knowledge or technique; and secondly because it is so attractive that the best achievements in this field suit the refined taste of professional mathematicians, the unaffected taste of amateurs, and the yet unsophisticated taste of inexperienced intelligent students. Moreover, due to the specific features of this field of study, with some luck, all of them, as well as the enthusiastic mathematics teachers, have more or less equal chances to make remarkable contributions. As in any other branch of mathematics, a talent, good luck and/or hard work, can produce real gems, but in GI the achievements are more visible, more tangible for simple mathematical folk’s appreciation, and have undoubted educational value. They are well ready for easy usage by mathematical educators both at school and university level, due to their main advantage: many of them are simple, but by no means trivial.