Triangle, n = 36 record
A = 0.003863346851034…
full precision
Exact value of the published coordinate literals:
0.00386334685103400502857985146511
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
65 triangles tied (within relative 10−9) at the minimal area, in 34 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.2020 · 0.2484 · 0.4491 |
(8,13,23) (10,15,25) |
| 2 | 0.1531 · 0.3798 · 0.5319 |
(8,18,35) (10,20,34) |
| 2 | 0.2140 · 0.3618 · 0.5752 |
(7,32,34) (9,33,35) |
| 2 | 0.2961 · 0.3263 · 0.6220 |
(0,10,27) (5,8,28) |
| 2 | 0.2016 · 0.5270 · 0.7281 |
(0,3,8) (1,5,10) |
| 2 | 0.1894 · 0.5537 · 0.7428 |
(0,12,25) (5,17,23) |
| 2 | 0.2639 · 0.4984 · 0.7620 |
(1,24,29) (3,26,29) |
| 2 | 0.3613 · 0.4106 · 0.7717 |
(6,9,19) (7,11,21) |
| 2 | 0.3595 · 0.4128 · 0.7721 |
(14,28,29) (16,27,29) |
| 2 | 0.3618 · 0.4106 · 0.7721 |
(6,9,33) (7,11,32) |
| 2 | 0.1125 · 0.7122 · 0.8242 |
(8,15,22) (10,13,31) |
| 2 | 0.3080 · 0.5537 · 0.8615 |
(0,25,26) (5,23,24) |
| 2 | 0.3740 · 0.4917 · 0.8655 |
(0,22,24) (5,26,31) |
| 2 | 0.2164 · 0.6827 · 0.8988 |
(7,15,24) (9,13,26) |
| 2 | 0.2699 · 0.6394 · 0.9091 |
(7,28,31) (9,22,27) |
| 2 | 0.2579 · 0.6557 · 0.9134 |
(6,25,27) (11,23,28) |
| 2 | 0.1785 · 0.7471 · 0.9254 |
(0,31,33) (5,22,32) |
| 2 | 0.2632 · 0.6841 · 0.9471 |
(6,15,29) (11,13,29) |
| 2 | 0.2079 · 0.7451 · 0.9528 |
(1,21,26) (3,19,24) |
| 2 | 0.2904 · 0.6720 · 0.9622 |
(1,13,25) (3,15,23) |
| 2 | 0.1696 · 0.8127 · 0.9820 |
(13,16,19) (14,15,21) |
| 2 | 0.4952 · 0.4979 · 0.9930 |
(0,18,28) (5,20,27) |
| 2 | 0.5161 · 0.5641 · 1.0801 |
(1,31,32) (3,22,33) |
| 2 | 0.1894 · 0.9181 · 1.1074 |
(12,24,25) (17,23,26) |
| 2 | 0.4861 · 0.6637 · 1.1498 |
(0,16,32) (5,14,33) |
| 2 | 0.3628 · 0.8127 · 1.1754 |
(13,16,35) (14,15,34) |
| 2 | 0.2474 · 0.9566 · 1.2039 |
(19,26,32) (21,24,33) |
| 2 | 0.1531 · 1.0826 · 1.2355 |
(18,22,35) (20,31,34) |
| 2 | 0.3613 · 0.8896 · 1.2509 |
(6,18,19) (11,20,21) |
| 2 | 0.3740 · 0.8773 · 1.2512 |
(0,24,34) (5,26,35) |
| 2 | 0.3914 · 0.8647 · 1.2560 |
(7,23,35) (9,25,34) |
| 1 | 0.1957 · 0.5518 · 0.7472 |
(2,5,21) |
| 1 | 0.2699 · 0.4956 · 0.7652 |
(2,22,27) |
| 1 | 0.3606 · 0.6966 · 1.0572 |
(4,21,25) |
Provenance
- Found by Nathan Sudermann-Merx, October 2026.
- Coordinates by an external contributor, re-verified here:
Nathan Sudermann-Merx search campaign, October 2026: C basin hopping with soft-min L-BFGS, symmetric orbit parametrisation, ruin-and-recreate moves, vertical seeding from n-1/n+1 records, HiGHS trust-region SLP polish— Found by vertical seeding / basin hopping; coordinates are the SLP-polished double-precision optimum, truncated toward zero.. - Verified in exact arithmetic: all 7140 triples enumerated, 65 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
