Square, n = 25 record
A = 0.008230069426525…
full precision
Exact value of the published coordinate literals:
0.00823006942652509338600432921683
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
44 triangles tied (within relative 10−9) at the minimal area, in 44 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0875 · 0.2234 · 0.2804 |
(0,8,22) |
| 1 | 0.1127 · 0.2416 · 0.3383 |
(1,2,11) |
| 1 | 0.0875 · 0.3198 · 0.3939 |
(0,5,8) |
| 1 | 0.1421 · 0.2999 · 0.4345 |
(21,23,24) |
| 1 | 0.1850 · 0.2994 · 0.4792 |
(12,22,24) |
| 1 | 0.1850 · 0.2999 · 0.4798 |
(12,23,24) |
| 1 | 0.1421 · 0.3628 · 0.4995 |
(17,21,23) |
| 1 | 0.1542 · 0.3671 · 0.5166 |
(5,6,14) |
| 1 | 0.2329 · 0.4069 · 0.6375 |
(1,10,23) |
| 1 | 0.2077 · 0.4326 · 0.6379 |
(10,13,20) |
| 1 | 0.2013 · 0.4665 · 0.6656 |
(3,5,22) |
| 1 | 0.2787 · 0.4168 · 0.6938 |
(1,4,16) |
| 1 | 0.2416 · 0.4566 · 0.6964 |
(1,11,13) |
| 1 | 0.3158 · 0.4069 · 0.7212 |
(9,10,23) |
| 1 | 0.3600 · 0.3671 · 0.7257 |
(6,14,23) |
| 1 | 0.2825 · 0.4566 · 0.7377 |
(3,11,13) |
| 1 | 0.2439 · 0.5086 · 0.7510 |
(3,7,8) |
| 1 | 0.1649 · 0.5938 · 0.7569 |
(13,15,22) |
| 1 | 0.3413 · 0.4382 · 0.7784 |
(4,19,23) |
| 1 | 0.2288 · 0.5648 · 0.7923 |
(11,19,24) |
| 1 | 0.3383 · 0.4598 · 0.7970 |
(2,11,16) |
| 1 | 0.2083 · 0.5938 · 0.8007 |
(13,15,16) |
| 1 | 0.3939 · 0.4359 · 0.8289 |
(0,5,7) |
| 1 | 0.3964 · 0.4568 · 0.8522 |
(10,14,15) |
| 1 | 0.2234 · 0.6472 · 0.8696 |
(0,17,22) |
| 1 | 0.2916 · 0.5803 · 0.8710 |
(18,21,22) |
| 1 | 0.3198 · 0.5618 · 0.8808 |
(5,8,16) |
| 1 | 0.3853 · 0.5194 · 0.9040 |
(16,19,21) |
| 1 | 0.3893 · 0.5214 · 0.9100 |
(17,18,20) |
| 1 | 0.3584 · 0.5559 · 0.9136 |
(8,12,17) |
| 1 | 0.3628 · 0.5984 · 0.9606 |
(2,17,23) |
| 1 | 0.2848 · 0.6768 · 0.9608 |
(8,15,23) |
| 1 | 0.4460 · 0.5167 · 0.9620 |
(0,9,12) |
| 1 | 0.3383 · 0.6353 · 0.9730 |
(2,7,11) |
| 1 | 0.2321 · 0.7797 · 1.0111 |
(7,13,21) |
| 1 | 0.2980 · 0.7148 · 1.0121 |
(5,9,24) |
| 1 | 0.4060 · 0.6105 · 1.0160 |
(4,6,8) |
| 1 | 0.2321 · 0.7882 · 1.0196 |
(7,13,23) |
| 1 | 0.2164 · 0.8080 · 1.0236 |
(4,20,22) |
| 1 | 0.4633 · 0.5690 · 1.0319 |
(9,13,14) |
| 1 | 0.3413 · 0.7379 · 1.0787 |
(4,9,19) |
| 1 | 0.2412 · 0.8544 · 1.0950 |
(3,17,24) |
| 1 | 0.3978 · 0.8089 · 1.2064 |
(9,16,18) |
| 1 | 0.3759 · 0.9218 · 1.2974 |
(0,1,19) |
Provenance
- Found by Rob Gardiner, September 2026.
- Coordinates by an external contributor, re-verified here:
Rob Gardiner, Heilbronn square configurations, September 2026.— Search from random starting configurations. - Verified in exact arithmetic: all 2300 triples enumerated, 44 tied at the minimum.
Record history
- 2026-07-23 0.00669+ — Tej Stead (first listed)
- 2026-07-31 0.006808+ — Marc-Emmanuel Coupvent des Graviers
- 2026-08-03 0.007110+ — Tej Stead
- 2026-08-18 0.007243+ — Nathan Sudermann-Merx
- 2026-08-20 0.007327+ — Nathan Sudermann-Merx, current record (coordinates and figure not public)
- 2026-08-20 0.0074071846 — independent search, this site (record)
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
