Viviani constant distance sum
Theorem.Viviani constant distance sum — d₁ + d₂ + d₃ = h — the distances from any interior point of an equilateral triangle sum to the altitude.
Proof.the sum of distances from an interior point of an equilateral triangle to its three sides equals the altitude √3/2, constant across 300 interior points — independent of the point.
Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.
src/9/1/index.ts#discoveredTheoremsWaveTwentySix
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
"Viviani constant distance sum" 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 discoveredTheoremsWaveTwentySix.
- 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 (discoveredTheoremsWaveTwentySix @ 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 discoveredTheoremsWaveTwentySix (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.