Sphere Volume Ratios in Tetrahedral and Triangular Patterns, and Some Implications
Carl R. Littmann
Although not obvious, there exists a volumetric ratio among big and small spheres in two basic tetrahedrally arrayed patterns that equals a basic spheres ratio in a somewhat similar triangular pattern. We display the cases. We show how the average of two volumetric ratios, using the most basic tetrahedrally and triangularly structured concentric spheres, equals the proton-to-electron mass ratio rather precisely. We outline how some of the above relates to some chemistry and physics, and discuss implications.
