Title
Distant Parents in Complete Binary Trees
Document Type
Article
Department or Administrative Unit
Mathematics
Publication Date
2013
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.
Recommended Citation
Glasby, S. P. (2013). Distant Parents in Complete Binary Trees. The Mathematical Scientist, 38, 7-16.
Journal
The Mathematical Scientist
Copyright
© Applied Probability Trust 2013
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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