Proof — Kepler conjecture (Hales' proof)
Statement
The densest packing of equal spheres in three dimensions is the face-centered cubic (FCC) and hexagonal close-packed (HCP) arrangements. Gold and platinum atoms achieve this optimal spatial configuration. Hales proved it using computer-assisted proof (Flyspeck project).
Formula
Maximum packing density = π/√18 ≈ 0.7405
Equation
FCC/HCP optimal
Proof sketch
Hales (1998): exhaustive case analysis with interval arithmetic. Formal verification completed 2014 (Flyspeck).
Source
Hales, The Kepler Conjecture, 1998. Flyspeck project, 2014.
Domains
mathematics, geometry