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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