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August 26, 2025˜The œFibonacci quarterly0 citations

The Best Two-Term Underapproximation Using Numbers From Fibonacci-Type Sequences

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MSMark Shiliaev

Key Points

  • The best two-term underapproximation is identified for specific θ values within (0,1].
  • Optimal sets of θ were determined, enhancing the understanding of two-term underapproximations.
  • This research employs Fibonacci and Lucas sequences, applying greedy algorithms to analyze numerical outcomes.
  • Implications suggest that these findings may improve calculations related to underapproximations in various mathematical contexts.

Abstract

This paper studies the greedy two-term underapproximation of θ∈(0,1] using reciprocals of numbers from a Fibonacci-type sequence (cn)n=1∞. We find the set of θ whose greedy two-term underapproximation is the best among all two-term underapproximations using 1/cn's. We then derive a neat description of the set when (cn)n=1∞ is the Fibonacci sequence or the Lucas sequence.

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Cite This Study

Mark Shiliaev (2025) studied this question.

synapsesocial.com/papers/68af620aad7bf08b1eae3101https://doi.org/10.1080/00150517.2025.2490766
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