number theory - The Four Square Theorem and Integral Apollonian Circle Packings, is there any connection? - Mathematics Stack Exchange

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I have been studying theta-functions and made an interesting observation which I have a question about QUESTION: Is there a more intuitive, in particular a mostly geometric way, to prove the four
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
Problem of Apollonius - Wikipedia
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
geometry - How the recursive structure of Apollonian gaskets can be described in order to be able to reproduce them? - Mathematics Stack Exchange
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
geometry - Impossible to pack Circles without gaps - Mathematics Stack Exchange
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
Problem of Apollonius - Wikipedia
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
The Euclidean Apollonian circle packing (−1,2,2,3)
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
PDF) A polytopal generalization of Apollonian packings and Descartes' theorem
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
Applications of Inversive Geometry
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
Apollonian circle packings: number theory - ScienceDirect
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
geometry - How the recursive structure of Apollonian gaskets can be described in order to be able to reproduce them? - Mathematics Stack Exchange
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