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
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
Counting Problems in Apollonian Circle Packings
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
geometry - Intuitively, why aren't all points in a circle covered in an Apollonian gasket? - Mathematics Stack Exchange
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
Crc concise encyclopedia of mathematics [part 1 of 4] e weisstein by okki kan - Issuu
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
PDF) Regular polytopes, sphere packings and Apollonian sections
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
fótMeij - International Mathematical Union
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
A Tisket, a Tasket, an Apollonian Gasket
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
retreat: I have been following the ups and downs
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