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
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number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
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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 - 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) Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
PDF) Elementary Number Theory
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
geometry - Frame challenge: Find the maximum $n$ such that circles of radius $1, rac12, rac13, , rac1n$ can be held immobile by a convex frame. - Mathematics Stack Exchange
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
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
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number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
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number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
February 2023 – Viewpoints which Matter
number theory - The Four Square Theorem and Integral Apollonian Circle  Packings, is there any connection? - Mathematics Stack Exchange
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