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

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Scientific Paper | |
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Title | Sphere Volume Ratios in Tetrahedral and Triangular Patterns, and Some Implications |

Read in full | Link to paper |

Author(s) | Carl R Littmann |

Keywords | {{{keywords}}} |

Published | 2011 |

Journal | Proceedings of the NPA |

Volume | 8 |

No. of pages | 3 |

Pages | 351-353 |

**Read the full paper** here

## 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.