−1, −2, −3……, Understand the Legacy

Abstract

Relations between arithmetic and geometric means will take center stage, so I thought it not amiss to devote a complete chapter to point out the ancient roots of these notions and the relations between seemingly disparate fields.

We may picture the product of three thousand years of geometric inventiveness in the form of a tree – the “Geometree” whose roots go back even further and whose branches represent the outcome of centuries of discovery and creation. With or without application, the branches and fruits of this tree are worth contemplating as a remarkable product of human imagination. The Geometree is healthy, vigorous and in full foliage, older than any redwood, and fully as majestic [34].

Robert Osserman