the golden angle is τ/φ² — the most irrational rotation
Theorem.the golden angle is τ/φ² — the most irrational rotation — GOLDEN_ANGLE_RAD = TAU/(PHI·PHI) identity;.
Proof.GOLDEN_ANGLE_RAD = TAU/(PHI·PHI) identity; φ²=φ+1; Fib approximants Euclidean quotients are 1s (CF [1;1,1,…] witness); equidistribution bound — golden min circular gap > 0 while rational 108° clumps at N=13. Bounded witness · pair golden/angle · claySolved via theorem.
Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.
src/3/7/index.ts#theGoldenAngleIsTauOverPhiSquaredTheMostIrrationalRotation
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
"the golden angle is τ/φ² — the most irrational rotation" 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 theGoldenAngleIsTauOverPhiSquaredTheMostIrrationalRotation.
- 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 (theGoldenAngleIsTauOverPhiSquaredTheMostIrrationalRotation @ src/3/7) 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 theGoldenAngleIsTauOverPhiSquaredTheMostIrrationalRotation (src/3/7/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.