A note on Farey sequences and Hausdorff dimension
classification
🧮 math-ph
cs.NAmath.MPmath.NAmath.NT
keywords
fareyclassesdimensionhausdorffsequencesalgebraicdefinedequation
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We prove that the Farey sequences can be express into equivalence classes labeled by a fractal parameter which looks like a Hausdorff dimension $h$ defined within the interval 1 < h < 2. The classes $h$ satisfy the same properties of the Farey series and for each value of $h$ there exists an algebraic equation.
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