Corpus ID: 119644969

Weighted Mediants and Fractals

@article{Aiylam2017WeightedMA,
  title={Weighted Mediants and Fractals},
  author={Dhroova Aiylam and Tanya Khovanova},
  journal={arXiv: Number Theory},
  year={2017}
}
  • Dhroova Aiylam, Tanya Khovanova
  • Published 2017
  • Mathematics
  • arXiv: Number Theory
  • In this paper we study a natural generalization of the Stern-Brocot sequences which comes from the introduction of weighted mediants. We focus our attention on the case $k = 3$, in which $(2a + c)/(2b + d)$ and $(a + 2c)/(b + 2d)$ are the two mediants inserted between $a/b$ and $c/d$. We state and prove several properties about the cross-differences of Stern-Brocot sequences with $k = 3$, and give a proof of the fractal-like rule that describes the cross-differences of the unit $k = 3$ Stern… CONTINUE READING

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