The distribution of rational numbers on Cantor's middle thirds set
Alexander Rahm, Noam Solomon, Tara Trauthwein, Barak Weiss
TL;DR
This paper investigates the distribution of rational numbers within Cantor's middle thirds set, providing a heuristic estimate and supporting it with extensive numerical data.
Contribution
It introduces a heuristic for counting reduced rationals in the Cantor set with bounded denominators and validates it through numerical computations.
Findings
Heuristic estimate for the number of rationals in the set
Numerical data supporting the heuristic
Insights into the distribution pattern of rationals
Abstract
We give a heuristic for the number of reduced rationals on Cantor's middle thirds set, with a fixed bound on the denominator. We also describe extensive numerical computations supporting this heuristic.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical functions and polynomials · semigroups and automata theory