Fibonacci numbers and a metric on coprime pairs
Mitsuaki Kimura
TL;DR
This paper introduces a new metric on coprime pairs of natural numbers and constructs a quasi-isometric embedding from natural numbers into this space using Fibonacci numbers.
Contribution
It presents a novel metric on coprime pairs and explicitly constructs a quasi-isometric embedding from natural numbers into this metric space.
Findings
Defined a new metric on coprime pairs
Constructed a quasi-isometric embedding using Fibonacci numbers
Established relationships between natural numbers and coprime pairs
Abstract
In this paper, we introduce a metric on the set of pairs of coprime natural numbers. We explicitly construct a quasi-isometric embedding from the set of natural numbers into this metric space via Fibonacci numbers.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Graph Labeling and Dimension Problems · Mathematical Dynamics and Fractals