Sphere Volume Ratios in Tetrahedral and Triangular Patterns, and Some Implications

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Scientific Paper
Title Sphere Volume Ratios in Tetrahedral and Triangular Patterns, and Some Implications
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Author(s) Carl R. Littmann
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Published 2011
Journal Proceedings of the NPA
Volume 8
No. of pages 3
Pages 351-353

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Abstract

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.