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
Apollonian network - Wikipedia
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
Mathematics Mind Map, PDF, Algebraic Geometry
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
PDF) Dismal Arithmetic
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
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
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
PDF) Geometric Sequences Of Discs In The Apollonian Packing
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
DMV-Jahrestagung 2015 in Hamburg
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
Indira's Pearls: Apollonian Gasket, Circle and Sphere Packing – Viewpoints which Matter
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
PDF) Dismal Arithmetic
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