A Fibonacci Theme on Balanced Binary Trees
نویسنده
چکیده
In this paper we show that, when a binary tree is in a certain critical balance, there emerge the Golden Ratio and the Fibonacci numbers. The paper consists of two sections. In the first section we find some elementary balance properties of optimal binary trees with variously weighted leaves. In the second section, a basic inequality implied by the optimality of trees is in turn used to define what we mean by "balanced" for a binary tree with leaves all weighted 1. The Fibonacci tree is then shown to be a highest balanced tree.
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