Leibniz and Wallis π series
Theorem.Leibniz and Wallis π series — π/4 = 1 − 1/3 + 1/5 − … and the Wallis product ∏(2n)²/((2n−1)(2n+1)) → π/2 both converge to π independently.
Proof.π/4 = 1 − 1/3 + 1/5 − … and the Wallis product ∏(2n)²/((2n−1)(2n+1)) → π/2 both converge to π independently — an alternating sum and an infinite product meeting at the same constant.
Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.
src/9/1/index.ts#discoveredTheoremsWaveTwentyNine
1 · Classification
bounded-witness — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Leibniz and Wallis π series" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveTwentyNine.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveTwentyNine @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveTwentyNine (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.