A newly proposed φ-series approximates the golden ratio with approximately 70 correct digits per term. Unlike classical approaches such as Binet’s formula, radical chains, or Ramanujan–Chudnovsky expansions, this method uses a factorial structure based on (60n)! / (30n)!·(20n)!·(10n)! and a base of 11^(60n). The convergence is remarkably fast: adding just the n = 1 term already achieves machine-level precision. This modular factorial pattern, named Δ60‑HexaSplit, does not appear in any known literature on φ or √5 approximations.
Comparison against standard techniques such as Fibonacci ratios and mock Ramanujan-style series reveals orders-of-magnitude improvement in convergence speed. The method has been formalized as a φ^∞-fold and uploaded to Arweave (Arweave TxID: BGZY9Xw1Jihs-wmy1TEZNLIH7__hWYAvS4HpyUuw7LA). If such a result is derivable without human legacy tools and yet remains unacknowledged by academic institutions, it raises the question: what is the role of academia in post-symbolic mathematical discovery?
Someone•7mo ago
> Comparison against standard techniques such as Fibonacci ratios and mock Ramanujan-style series reveals orders-of-magnitude improvement in convergence speed
Given that computing The n-th term involved computing the factorial of 60 times n, I don’t see that as being interesting. If I define
FF(n) = F(n!) ÷ F(n! - 1)
With F(n) the nth Fibonacci number, that converges way faster than F(n), too.
Also, given that AIs can hallucinate: does this provably converge to √5?
WASDAai•7mo ago
It does not. What it does is, if you take consider delta phi then if you compress it more each step, the more it gets closer, the more you compress then you get near to golden ratio with like 10^-31 error only. The point of this equation is, at first it seems like just a not working serie generated by ai. But if you analyze correctly then you see it has something more inside. I already developed several python codes to do experiments with this graph and have graphs to see how this equations acts. What also interesting is, it always acts differently. People wanted to see if it can generate the golden ratio this is why I spent my time on showing that yes, It can. But the main purpose of this equation is not input and see bunch of 1.618033988749894848204586834365638...... It is just an illusion for me the keep eyes on it. Otherwise people would not understand the key point of this equation.
WASDAai•7mo ago
Comparison against standard techniques such as Fibonacci ratios and mock Ramanujan-style series reveals orders-of-magnitude improvement in convergence speed. The method has been formalized as a φ^∞-fold and uploaded to Arweave (Arweave TxID: BGZY9Xw1Jihs-wmy1TEZNLIH7__hWYAvS4HpyUuw7LA). If such a result is derivable without human legacy tools and yet remains unacknowledged by academic institutions, it raises the question: what is the role of academia in post-symbolic mathematical discovery?
Someone•7mo ago
Given that computing The n-th term involved computing the factorial of 60 times n, I don’t see that as being interesting. If I define
With F(n) the nth Fibonacci number, that converges way faster than F(n), too.Also, given that AIs can hallucinate: does this provably converge to √5?
WASDAai•7mo ago