  The famous Kepler conjecture has a less spectacular, two-dimensional
equivalent: The theorem of Thue states that the densest circle packing in the
Euclidean plane has a hexagonal structure. A common proof uses Voronoi cells
and analyzes their area applying Jensen's inequality on convex functions to
receive a local estimate which is globally valid. Based on the concept of
Voronoi cells, we will introduce a new tessellation into so-called L-triangles
which can be related to fundamental parallelograms of lattice circle packings.
Therefore a globally disordered circle packing can be reduced to locally
ordered configurations: We will show how the theorem of Lagrange on lattice
circle packings can be applied to non-lattice circle packings. Thus we receive
a new proof of Thue's theorem.
