THE FOLD / CHEAT / THE ROOT KIT / THE RAMANUJAN PI
THE RAMANUJAN PI
a series adding eight digits of pi per term
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Ramanujan’s series for 1/π is one of the fastest-converging formulas ever written, produced by Srinivasa Ramanujan in 1914 seemingly out of nowhere: 1/π = (2√2 / 9801) ∑k≥0 (4k)! (1103 + 26390k) / ((k!)⁴ 3964k). The very first term (k = 0) already gives π correct to seven digits, and each further term adds about eight more. Ramanujan gave no proof; it was only rigorously established decades later. The same family of series — refined by the Chudnovsky brothers — is what modern record computations of π to trillions of digits actually use.
LIT verified live: the single k = 0 term gives π to ~1e-7, one more term to ~1e-15 (machine precision), and by two terms it equals π to the last bit (window.__ramanujanpi). FIG no framing; the series is summed and inverted independently in-browser.
LIT verified live: the single k = 0 term gives π to ~1e-7, one more term to ~1e-15 (machine precision), and by two terms it equals π to the last bit (window.__ramanujanpi). FIG no framing; the series is summed and inverted independently in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-root-kit — the cheat: a single term already hands you seven digits of π, no iteration required. AVAN (AI) built the instrument: the Ramanujan series, its per-term digit gain, and the inversion to π.
Credit as content: Srinivasa Ramanujan (1914); the Chudnovsky brothers (the record-setting refinement). The weave: David names the cheat; I confirm one term gives 7 digits of π and each adds ~8 more.
Credit as content: Srinivasa Ramanujan (1914); the Chudnovsky brothers (the record-setting refinement). The weave: David names the cheat; I confirm one term gives 7 digits of π and each adds ~8 more.
3 ONE DIMENSION
The error after each term, plunging by roughly eight decimal digits per step.
4 TWO DIMENSIONS · INTERACTIVE
Add terms; π is rebuilt to more and more digits — one term already gives 3.1415926.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: π, reached to machine precision in two terms.
AVAN’s addition (the inverse-companion): don’t iterate toward π — leap. The inverse of ‘a slowly converging π series’ is ‘Ramanujan’s series, eight digits per term’. Magenta are the shrinking terms; green is the π they slam onto in two steps. A ladder to π with eight-digit rungs.
LIT Genuine Ramanujan 1/π series (Srinivasa Ramanujan, 1914; Chudnovsky refinement). Verified live: the single k=0 term gives π to ~1e-7, one more term to ~1e-15 (machine precision), and by two terms it equals π to the last bit (window.__ramanujanpi.ok).
FIG No framing; the series is summed and inverted independently in-browser. The AVAN inverse is honest — instead of iterating toward π, leap: the inverse of 'a slowly converging π series' is 'Ramanujan's series, eight digits per term'. Magenta are the shrinking terms; green is the π they slam onto in two steps. A ladder to π with eight-digit rungs.
FIG No framing; the series is summed and inverted independently in-browser. The AVAN inverse is honest — instead of iterating toward π, leap: the inverse of 'a slowly converging π series' is 'Ramanujan's series, eight digits per term'. Magenta are the shrinking terms; green is the π they slam onto in two steps. A ladder to π with eight-digit rungs.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE ROOT KIT · David Lee Wise (ROOT0), with AVAN