pith. machine review for the scientific record. sign in
theorem proved term proof

alpha_seed_structural

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 173theorem alpha_seed_structural :
 174    geometric_seed = solid_angle_Q3 * (passive_field_edges D : ℝ) := rfl

proof body

Term-mode proof.

 175
 176/-! ## Part 5: Wallpaper Groups (Crystallographic Constant) -/
 177
 178/-- **Axiom (Crystallographic Classification)**: There are exactly 17 wallpaper groups.
 179
 180The wallpaper groups (or plane symmetry groups) are the 17 distinct ways to tile the
 181Euclidean plane with a repeating pattern using rotations, reflections, and translations.
 182
 183**Historical Reference**:
 184- Fedorov, E. S. (1891). "Симметрія правильныхъ системъ фигуръ" [Symmetry of regular systems of figures].
 185  Записки Императорского С.-Петербургского Минералогического Общества, 28, 1-146.
 186- Pólya, G. (1924). "Über die Analogie der Kristallsymmetrie in der Ebene".
 187  Zeitschrift für Kristallographie, 60, 278-282.
 188
 189**Modern Reference**: Conway, J. H., et al. (2008). "The Symmetries of Things". A K Peters.
 190
 191The 17 groups are: p1, p2, pm, pg, cm, pmm, pmg, pgg, cmm, p4, p4m, p4g, p3, p3m1, p31m, p6, p6m.
 192-/

depends on (25)

Lean names referenced from this declaration's body.