Triangle, n = 17 record
A = 0.016242328407103…
full precision
Exact value of the published coordinate literals:
0.0162423284071037960150427736551
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
28 triangles tied (within relative 10−9) at the minimal area, in 28 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.2571 · 0.2837 · 0.5265 |
(10,15,16) |
| 1 | 0.2534 · 0.3535 · 0.5968 |
(6,9,12) |
| 1 | 0.2534 · 0.3836 · 0.6282 |
(3,6,9) |
| 1 | 0.1875 · 0.4642 · 0.6420 |
(3,5,15) |
| 1 | 0.2145 · 0.4459 · 0.6517 |
(0,2,13) |
| 1 | 0.3216 · 0.4217 · 0.7379 |
(0,5,9) |
| 1 | 0.3267 · 0.4642 · 0.7864 |
(3,14,15) |
| 1 | 0.3022 · 0.4900 · 0.7877 |
(1,9,15) |
| 1 | 0.2070 · 0.5858 · 0.7872 |
(8,12,16) |
| 1 | 0.3715 · 0.4655 · 0.8333 |
(1,5,7) |
| 1 | 0.3345 · 0.5155 · 0.8464 |
(6,10,14) |
| 1 | 0.4217 · 0.4679 · 0.8866 |
(2,5,9) |
| 1 | 0.3695 · 0.5446 · 0.9112 |
(1,3,11) |
| 1 | 0.2564 · 0.7025 · 0.9558 |
(4,5,10) |
| 1 | 0.1689 · 0.8040 · 0.9688 |
(2,7,15) |
| 1 | 0.3535 · 0.6965 · 1.0480 |
(6,12,15) |
| 1 | 0.5192 · 0.5446 · 1.0621 |
(1,3,8) |
| 1 | 0.3302 · 0.7379 · 1.0661 |
(0,9,16) |
| 1 | 0.4042 · 0.6709 · 1.0733 |
(3,7,16) |
| 1 | 0.4900 · 0.6431 · 1.1317 |
(9,11,15) |
| 1 | 0.4459 · 0.6881 · 1.1325 |
(0,12,13) |
| 1 | 0.5484 · 0.6123 · 1.1594 |
(7,11,13) |
| 1 | 0.5829 · 0.5858 · 1.1674 |
(12,14,16) |
| 1 | 0.4678 · 0.7106 · 1.1770 |
(4,6,11) |
| 1 | 0.4224 · 0.7872 · 1.2082 |
(4,8,16) |
| 1 | 0.4314 · 0.8333 · 1.2635 |
(1,7,12) |
| 1 | 0.3267 · 0.9688 · 1.2942 |
(2,14,15) |
| 1 | 0.6517 · 0.7313 · 1.3822 |
(2,8,13) |
Provenance
- Found by Fable 5.1 with Shengtong Zhang, September 2026.
- Coordinates by an external contributor, re-verified here:
Fable51 search campaign, September 2026: symmetry-reduced basin hopping (orbit parametrization, greedy ruin-and-recreate, soft-min warm-up, trust-region SLP) and insertion ladders from neighbouring records; tie system refined to 80 digits by damped Gauss-Newton; verified in exact rational arithmetic— not symmetric; 28 tied minimal triangles. - Verified in exact arithmetic: all 680 triples enumerated, 28 tied at the minimum.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
