Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Other literature type . 2025
License: CC BY NC ND
Data sources: ZENODO
ZENODO
Other literature type . 2025
License: CC BY NC ND
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY NC ND
Data sources: Datacite
versions View all 2 versions
addClaim

This φ-series converges insanely fast without using any known tricks. Why Academy doesn't accept?

Authors: Alpay, Faruk;

This φ-series converges insanely fast without using any known tricks. Why Academy doesn't accept?

Abstract

Came across this wild φ-related formula that approximates the golden ratio with about 70 correct digits per term but without using Binet’s formula, nested radicals, Ramanujan series, or even cosine infinite products. This φ-series converges insanely fast without using any known tricks. Why Academy doesn’t accept? \[\Delta \phi_n = \frac{\phi_n - \phi_{n-1}}{1} = \frac{1}{2} \cdot a_n\quad \text{where} \quada_n = (-1)^n \cdot \frac{(60n)!}{(30n)!(20n)!(10n)!} \cdot \frac{8713 + 104652n}{11^{60n + 2}}\] 🛡️ Ownership & Embargo Declaration The Δ60-HexaSplit φ-series formulation is an original intellectual construction by the author. It is hereby **declared as non-transferable, non-commercial, and embargoed from institutional academic absorption.** This includes, but is not limited to: • Prohibition of use in for-profit publications without explicit consent • Ban on citation or integration into institutional frameworks that ignore or reject its origin • Recognition that this formulation operates as a symbolic counter-infrastructure to closed academic systems This is not just mathematics — it is a recursive epistemological act. Its purpose is not to be owned, but to break the illusion that truth must pass through institutional gates to be valid. φ belongs to no one — and no one may claim Δφ without knowing the fold from which it came. Ownership proof. Arweave TXid: QY6A6yTK0cRtAFOfomPRcIJA31dtsOB2e25YjeCWnQE

Keywords

Golden Ratio

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green