Napoleon triangle theorem
Theorem.Napoleon triangle theorem — |N₁N₂| = |N₂N₃| = |N₃N₁| — the centroids of outward equilateral triangles on any triangle’s sides are themselves equilateral.
Proof.the centroids of outward equilateral triangles on the sides of any triangle form an equilateral triangle, confirmed on ~200 non-degenerate triangles (equal pairwise centroid distances to 1e-6).
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
"Napoleon triangle theorem" 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.