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arXiv · 1603.06307

The golden ratio, Fibonacci numbers and BBP-type formulas

Kunle Adegoke
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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-ratio-base BBP-type formulas for some mathematical constants, including $\pi$, $\log 2$, $\log\phi$ and $\sqrt 2\,\arctan\sqrt 2$. The $\phi-$nary BBP-type formulas derived here are considerably simpler than similar results contained in earlier literature.

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Kunle Adegoke. 2016-03-21. The golden ratio, Fibonacci numbers and BBP-type formulas. https://arxiv.org/abs/1603.06307

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