Square, n = 35 record
A = 0.004432287444307…
full precision
Exact value of the published coordinate literals:
0.00443228744430732418587361132274
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
64 triangles tied (within relative 10−9) at the minimal area, in 64 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0585 · 0.1912 · 0.2316 |
(17,22,25) |
| 1 | 0.0658 · 0.1835 · 0.2333 |
(20,28,30) |
| 1 | 0.0946 · 0.1709 · 0.2554 |
(3,4,7) |
| 1 | 0.1185 · 0.2499 · 0.3648 |
(4,9,29) |
| 1 | 0.1577 · 0.3443 · 0.5006 |
(6,16,26) |
| 1 | 0.1849 · 0.3260 · 0.5096 |
(18,27,34) |
| 1 | 0.1709 · 0.3437 · 0.5133 |
(3,4,26) |
| 1 | 0.1553 · 0.3720 · 0.5260 |
(16,21,24) |
| 1 | 0.1835 · 0.3587 · 0.5411 |
(2,20,30) |
| 1 | 0.1841 · 0.3677 · 0.5507 |
(10,19,28) |
| 1 | 0.1876 · 0.3997 · 0.5865 |
(10,20,27) |
| 1 | 0.2164 · 0.3711 · 0.5867 |
(0,14,21) |
| 1 | 0.2049 · 0.3874 · 0.5915 |
(3,8,23) |
| 1 | 0.2676 · 0.3277 · 0.5945 |
(14,29,31) |
| 1 | 0.2270 · 0.3708 · 0.5970 |
(2,24,34) |
| 1 | 0.2499 · 0.3728 · 0.6221 |
(4,9,31) |
| 1 | 0.1709 · 0.4615 · 0.6316 |
(3,4,6) |
| 1 | 0.2568 · 0.3850 · 0.6412 |
(21,29,32) |
| 1 | 0.2391 · 0.4182 · 0.6567 |
(16,18,23) |
| 1 | 0.2018 · 0.4615 · 0.6627 |
(3,6,17) |
| 1 | 0.1841 · 0.4833 · 0.6667 |
(19,22,28) |
| 1 | 0.2447 · 0.4276 · 0.6718 |
(1,12,16) |
| 1 | 0.2004 · 0.4791 · 0.6789 |
(7,9,21) |
| 1 | 0.1545 · 0.5278 · 0.6815 |
(23,24,31) |
| 1 | 0.1609 · 0.5247 · 0.6849 |
(0,23,29) |
| 1 | 0.2376 · 0.4534 · 0.6905 |
(3,11,16) |
| 1 | 0.1511 · 0.5491 · 0.6995 |
(10,12,22) |
| 1 | 0.1780 · 0.5260 · 0.7034 |
(16,21,33) |
| 1 | 0.3437 · 0.3718 · 0.7151 |
(3,22,26) |
| 1 | 0.3346 · 0.3853 · 0.7194 |
(15,18,28) |
| 1 | 0.3397 · 0.3825 · 0.7217 |
(0,7,11) |
| 1 | 0.1944 · 0.5312 · 0.7251 |
(6,15,27) |
| 1 | 0.3640 · 0.3658 · 0.7294 |
(18,20,22) |
| 1 | 0.3328 · 0.3997 · 0.7321 |
(10,25,27) |
| 1 | 0.3453 · 0.3932 · 0.7380 |
(2,27,32) |
| 1 | 0.2605 · 0.4783 · 0.7384 |
(1,2,15) |
| 1 | 0.2567 · 0.4906 · 0.7469 |
(5,27,28) |
| 1 | 0.1637 · 0.6461 · 0.8093 |
(12,15,34) |
| 1 | 0.2439 · 0.6316 · 0.8753 |
(4,6,25) |
| 1 | 0.4007 · 0.4853 · 0.8857 |
(11,29,34) |
| 1 | 0.2860 · 0.6040 · 0.8898 |
(1,27,29) |
| 1 | 0.2316 · 0.6667 · 0.8980 |
(17,22,28) |
| 1 | 0.2391 · 0.6625 · 0.9014 |
(8,13,26) |
| 1 | 0.2546 · 0.6563 · 0.9107 |
(13,14,30) |
| 1 | 0.2477 · 0.6632 · 0.9107 |
(11,19,21) |
| 1 | 0.2568 · 0.6789 · 0.9355 |
(7,21,32) |
| 1 | 0.2164 · 0.7231 · 0.9393 |
(4,14,21) |
| 1 | 0.3656 · 0.5779 · 0.9432 |
(6,18,30) |
| 1 | 0.3620 · 0.5865 · 0.9482 |
(10,17,20) |
| 1 | 0.3846 · 0.5808 · 0.9652 |
(2,14,19) |
| 1 | 0.1535 · 0.8141 · 0.9672 |
(12,20,29) |
| 1 | 0.4642 · 0.5303 · 0.9944 |
(6,23,34) |
| 1 | 0.4576 · 0.5386 · 0.9960 |
(8,17,24) |
| 1 | 0.3481 · 0.6694 · 1.0173 |
(17,26,29) |
| 1 | 0.3292 · 0.7077 · 1.0368 |
(11,28,31) |
| 1 | 0.3276 · 0.7171 · 1.0445 |
(16,25,29) |
| 1 | 0.4050 · 0.6439 · 1.0488 |
(5,19,29) |
| 1 | 0.1637 · 0.9009 · 1.0644 |
(12,17,34) |
| 1 | 0.5205 · 0.5936 · 1.1140 |
(4,8,19) |
| 1 | 0.5342 · 0.5915 · 1.1255 |
(3,23,28) |
| 1 | 0.5251 · 0.6068 · 1.1318 |
(1,9,30) |
| 1 | 0.3951 · 0.7487 · 1.1436 |
(5,17,21) |
| 1 | 0.5448 · 0.6032 · 1.1479 |
(13,23,25) |
| 1 | 0.2775 · 1.0264 · 1.3038 |
(15,17,32) |
Provenance
- Found by Rob Gardiner, September 2026.
- Coordinates by an external contributor, re-verified here:
Rob Gardiner, Heilbronn square configurations, September 2026; original starting configuration: https://math.tejstead.com/heilbronn/square/34/.— Further optimisation of our n=35 construction derived from the published n=34 configuration credited to Fable 5.1 with Shengtong Zhang.. - Verified in exact arithmetic: all 6545 triples enumerated, 64 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
