Triangle, n = 7 proven
A =
= 0.0972222222222222222222222222222222222222222222…
Classes
Symmetry
Symmetry
120° Rotationally symmetric (group C3, order 3).
7 points in 3 orbits (3 + 3 + 1) — hover a point to see its orbit.
Minimal triangles
9 triangles tied (within relative 10−9) at the minimal area, in 3 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 3 | 0.3351 · 0.5803 · 0.6701 |
(0,2,6) (1,3,6) (4,5,6) | |
| 3 | 0.3351 · 0.8865 · 1.1607 |
(0,1,3) (0,2,4) (3,4,5) | |
| 3 | 0.5803 · 0.6701 · 1.2081 |
(0,5,6) (1,4,6) (2,3,6) |
Provenance
- Found by David Cantrell, July 2006.
- Proved optimal by Z. Zeng and L. Chen, 2019.
- Coordinates exact, as published in:
arXiv:2607.15021. - Verified in exact arithmetic: all 35 triples enumerated, 9 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
