A Closed Form Transcendental Formulation for the Golden Ratio using a Hyperbolic Convergence Sequence

This paper introduces a closed-form transcendental formulation that converges monotonically to the Golden Ratio. The formulation is constructed by embedding a nested hyperbolic tangent expression within an arctangent function to isolate a continuous transcendental coefficient.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-07
DOI
https://doi.org/10.5281/zenodo.24025046
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
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preprint

A Closed Form Transcendental Formulation for the Golden Ratio using a Hyperbolic Convergence Sequence

Bheema Varanasi
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Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

A Closed Form Transcendental Formulation for the Golden Ratio using a Hyperbolic Convergence Sequence

Bheema Varanasi
preprint en

Abstract

This paper introduces a closed-form transcendental formulation that converges monotonically to the Golden Ratio. The formulation is constructed by embedding a nested hyperbolic tangent expression within an arctangent function to isolate a continuous transcendental coefficient.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
DOIOpen Access PDFOpenAlex
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