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We define the “coronas”, which are especially spiky paths in the Farey graphFarey graph going from \(\underline{0}=(1,0)\) to \(\underline{\infty }=(0,1)\) . We show that for \(R\ge 2\) , \(\left\{ (x,y)\in \mathbb {N}^{+}\times \mathbb {N}^{+},\right. \) \(\left. \gcd (x,y)=1, \; x+y\le R \right\} \) is a corona.

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Meditations on the Farey Fractal

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  • 出版模式：

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  • 发表日期：

    2026年

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  • Shai Haran

摘要

We define the “coronas”, which are especially spiky paths in the Farey graphFarey graph going from \(\underline{0}=(1,0)\) to \(\underline{\infty }=(0,1)\) . We show that for \(R\ge 2\) , \(\left\{ (x,y)\in \mathbb {N}^{+}\times \mathbb {N}^{+},\right. \) \(\left. \gcd (x,y)=1, \; x+y\le R \right\} \) is a corona.