Distant Parents in Complete Binary Trees

Department or Administrative Unit

Mathematics

Document Type

Article

Author Copyright

© Applied Probability Trust 2013

Publication Date

2013

Journal

The Mathematical Scientist

Abstract

There is a unique path from the root of a tree to any other vertex. Every vertex, except the root, has a parent: the adjoining vertex on this unique path. This is the conventional definition of the parent vertex. For complete binary trees, however, we show that it is useful to define another parent vertex, called a distant parent. The study of distant parents leads to novel connections with dyadic rational numbers. Moreover, we apply the concepts of close and distant parent vertices to deduce an apparently new sense in which continued fractions are ‘best’ rational approximations.

Comments

This article was originally published in The Mathematical Scientist. The full-text article from the publisher can be found here.

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