Heron formula vs coordinate area
Theorem.Heron formula vs coordinate area — area = √(s(s−a)(s−b)(s−c)) matches the shoelace area.
Proof.area = √(s(s−a)(s−b)(s−c)) matches the shoelace area for EVERY integer triangle with sides ≤ 20, and gives integer-area Heronian triangles ((3,4,5) → 6) — area from the three sides alone.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveThirtyFive
1 · Classification
finite-complete — 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
"Heron formula vs coordinate area" 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 discoveredTheoremsWaveThirtyFive.
- 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 (discoveredTheoremsWaveThirtyFive @ 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 discoveredTheoremsWaveThirtyFive (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.