Square, n = 10 record
A = 0.046537419582541…
full precision
Exact value of the published coordinate literals:
0.0465374195825417294326266114236
Classes
Symmetry
Symmetry
2-fold dihedral symmetry (group D2, order 4). (Friedman's page says: symmetric about both diagonals.)
Minimal triangles
16 triangles tied (within relative 10−9) at the minimal area, in 4 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 4 | 0.2232 · 0.5898 · 0.7641 |
(0,1,2) (0,2,6) (3,7,9) (7,8,9) | |
| 4 | 0.3219 · 0.5215 · 0.8093 |
(1,4,5) (3,4,5) (4,5,6) (4,5,8) | |
| 4 | 0.3219 · 0.7023 · 1.0045 |
(0,5,8) (1,4,9) (2,3,4) (5,6,7) | |
| 4 | 0.3219 · 0.8093 · 1.1159 |
(1,4,8) (1,5,8) (3,4,6) (3,5,6) |
Provenance
- Found by F. Comellas and J. Yebra, December 2001.
- Coordinates from spiralulam/heilbronn (MIT):
spiralulam/heilbronn config_n10.json— Comellas and Yebra (2002). - Verified in exact arithmetic: all 120 triples enumerated, 16 tied at the minimum.
- Friedman's page lists:
A = .04654+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
