Triangle, n = 9 record
A =
= 0.0548469387755102040816326530612244897959183673…
Classes
Symmetry
Symmetry
120° Rotationally symmetric (group C3, order 3).
9 points in 3 orbits (3 + 3 + 3) — hover a point to see its orbit.
Minimal triangles
13 triangles tied (within relative 10−9) at the minimal area, in 5 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 3 | 0.1779 · 0.6164 · 0.6416 |
(0,4,7) (1,5,8) (2,3,6) | |
| 3 | 0.1779 · 0.6416 · 0.7118 |
(0,4,8) (1,5,6) (2,3,7) | |
| 3 | 0.3559 · 0.6164 · 0.9416 |
(3,6,8) (4,6,7) (5,7,8) | |
| 3 | 0.6416 · 0.7118 · 1.3435 |
(0,3,7) (1,4,8) (2,5,6) | |
| 1 | 0.3559 · 0.3559 · 0.3559 |
(6,7,8) |
Provenance
- Found by David Cantrell, July 2006.
- Coordinates generated from the exact construction:
data/sources/exact/constructions.py— exact rational configuration on a 1/56 grid, value exactly 43/784; identified here from the reconstruction's convergence. - Verified in exact arithmetic: all 84 triples enumerated, 13 tied at the minimum.
Record history
- 2026-08-22 coordinates identified as exact rationals on a 1/56 grid (value exactly 43/784); replaces the reconstruction (this site)
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
