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arXiv 2009.02680math.MGmath-phmath.MPmath.NT
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阿波罗深度、旋量和超戴德金镶嵌

Apollonian depth, spinors, and the super-Dedekind tessellation

Jerzy Kocik

摘要:

三轮的位形空间(三个接触的圆盘)与复平面重合,从而得到一个由相切和泡利旋量构成的射影空间。值得注意的是,深度函数的分形呈现出一种特别简单而优雅的形式。此外,由于一定的对称群的商空间提供了一个参数化的阿波罗磁盘包装。

英文摘要:

The configuration space of tricycles (triples of disks in contact) is shown to coincide with the complex plane resulting as a projective space costructed from the tangency and Pauli spinors. Remarkably, the fractal of the depth functions assumes a particularly simple and elegant form. Moreover, the factor space due to a certain symmetry group provides a parametrization of the Apollonian disk packings.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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