2016
DOI: 10.48550/arxiv.1603.06307
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The golden ratio, Fibonacci numbers and BBP-type formulas

Kunle Adegoke

Abstract: We derive interesting arctangent identities involving the golden ratio, Fibonacci numbers and Lucas numbers. Binary BBP-type formulas for the arctangents of certain odd powers of the golden ratio are also derived, for the first time in the literature. Finally we derive golden-ratiobase BBP-type formulas for some mathematical constants, including π, log 2, log φ and √ 2 arctan √ 2. The φ−nary BBP-type formulas derived here are considerably simpler than similar results contained in earlier literature.

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