Square, n = 17 record
A = 0.017261677072523…
full precision
Exact value of the published coordinate literals:
0.0172616770725236010888553888455
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
27 triangles tied (within relative 10−9) at the minimal area, in 27 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.2129 · 0.2158 · 0.3906 |
(0,2,8) |
| 1 | 0.1171 · 0.4080 · 0.4962 |
(3,6,10) |
| 1 | 0.2872 · 0.3096 · 0.5851 |
(0,13,15) |
| 1 | 0.2172 · 0.3990 · 0.6045 |
(5,11,16) |
| 1 | 0.2647 · 0.3972 · 0.6530 |
(7,14,16) |
| 1 | 0.3163 · 0.3918 · 0.7011 |
(0,9,11) |
| 1 | 0.3345 · 0.3990 · 0.7273 |
(4,5,16) |
| 1 | 0.3497 · 0.3840 · 0.7276 |
(2,7,15) |
| 1 | 0.3456 · 0.4254 · 0.7656 |
(10,12,15) |
| 1 | 0.2740 · 0.5155 · 0.7841 |
(1,5,6) |
| 1 | 0.3829 · 0.4254 · 0.8037 |
(9,12,15) |
| 1 | 0.2129 · 0.6362 · 0.8439 |
(2,8,10) |
| 1 | 0.2647 · 0.6045 · 0.8648 |
(11,14,16) |
| 1 | 0.4080 · 0.4928 · 0.8975 |
(3,6,16) |
| 1 | 0.2714 · 0.6658 · 0.9336 |
(5,7,12) |
| 1 | 0.3456 · 0.6278 · 0.9706 |
(0,10,12) |
| 1 | 0.2418 · 0.7361 · 0.9744 |
(1,10,16) |
| 1 | 0.3854 · 0.6278 · 1.0108 |
(0,3,12) |
| 1 | 0.3670 · 0.6501 · 1.0147 |
(4,7,9) |
| 1 | 0.4541 · 0.6177 · 1.0698 |
(4,8,13) |
| 1 | 0.3497 · 0.7226 · 1.0701 |
(2,15,16) |
| 1 | 0.5022 · 0.6357 · 1.1362 |
(3,9,13) |
| 1 | 0.2872 · 0.8628 · 1.1479 |
(0,4,15) |
| 1 | 0.4541 · 0.7394 · 1.1920 |
(8,13,14) |
| 1 | 0.3381 · 0.9055 · 1.2420 |
(3,7,11) |
| 1 | 0.5160 · 0.7550 · 1.2698 |
(10,11,13) |
| 1 | 0.3775 · 0.8986 · 1.2747 |
(1,2,14) |
Provenance
- Found by Chouaieb Nemri (AlphaEvolve, Google Cloud), August 2026.
- Found with AlphaEvolve (Google Cloud) and submitted in August 2026, superseding the previous
.016481+record (Tej Stead). - Coordinates by an external contributor, re-verified here:
github.com/cnemri/heilbronn-alphaevolve— independently re-verified in exact arithmetic by this site. - Verified in exact arithmetic: all 680 triples enumerated, 27 tied at the minimum.
Record history
- 2026-07 0.016481+ — Tej Stead
- 2026-08-03 0.0172616771 — cnemri via AlphaEvolve (verified here; record)
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
