Triangle, n = 11 record
A = 0.036529889880029…
full precision
Exact value of the published coordinate literals:
0.036529889880029800850674405395
Symmetry
Symmetry
Mirror symmetric (group D1, order 2). (Friedman's page says: reflectional symmetry.)
Minimal triangles
17 triangles tied (within relative 10−9) at the minimal area, in 9 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.3731 · 0.4598 · 0.8131 |
(0,3,9) (3,4,10) |
| 2 | 0.3731 · 0.4662 · 0.8199 |
(3,4,5) (3,8,9) |
| 2 | 0.2817 · 0.6764 · 0.9428 |
(2,5,8) (5,6,8) |
| 2 | 0.2881 · 0.8515 · 1.1298 |
(0,1,6) (2,7,10) |
| 2 | 0.4598 · 0.6970 · 1.1495 |
(0,5,9) (4,8,10) |
| 2 | 0.5395 · 0.6351 · 1.1679 |
(1,2,3) (3,6,7) |
| 2 | 0.5213 · 0.6970 · 1.2122 |
(0,4,8) (5,9,10) |
| 2 | 0.5213 · 0.7248 · 1.2403 |
(0,2,4) (6,9,10) |
| 1 | 0.5395 · 0.5395 · 1.0704 |
(1,3,7) |
Provenance
- Found by AlphaEvolve, June 2025.
- Coordinates as published by AlphaEvolve (Google DeepMind):
google-deepmind/alphaevolve_results (arXiv:2506.13131)— converted from the equilateral frame. - Verified in exact arithmetic: all 165 triples enumerated, 17 tied at the minimum.
- Friedman's page lists:
A = .03652+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
