Papers

The list is split into two groups:

1.  Geometry of disk arrangements

2.  Spinors in disk arrangements 

1. Descartes, Apollonian,
    and other disk configurations

For the theorem on the disks in general configuration, see 

• A theorem on circle configurations  
  arXiv:0706.0372  (2007, 16 pages).

For the above interpreted as the (possibly) simplest proof of Descartes' formula, see

• Proof of Descartes circle formula and its generalization clarified 
  [arXiv:1910.09174] (2019, 3 pages) 

Applications of the generalized formula 

• Lens sequences, 
  Journal of Integer Sequences, Vol 23 (2020), Article 20.11.6  (36 pages)

• The Koide Lepton Mass Formula and Geometry of Circle Configurations,
  (2012, 3 pages) [arXiv:1201.2067]   [Cited in the Wikipedia]

• On the Dedekind tessellation,
  [arXiv:1912.05768] (2019, 16 pages)

Other papers related to disk arrangements

• On a Diophantine equation that generates all integral Apollonian gaskets, ISRN Geometry.Article ID 348618, 19 pages, 2012. doi:10.5402/2012/348618.
  [arXiv:2008.04440]

• Apollonian depth and the accidental fractal, (2020, 35 pages]
  [arXiv:2002.04135] 

• Fibonacci numbers and Ford circles (2020, 8 pages) 
  [arXiv: 2003.00852]

• A note on unbounded Apollonian disk packings
  [arXiv:1910.05924] 

• Coupled-ring resonance and unitary groups (with M. Sayeh), The Journal of the Optical Society of America B, 36 (3), 2019, 667-673.
  [arXiv:1807.06773]

• Skein relations for spin networks, modified, Journal of Knot Theory and Its Ramifications, 27 (7) 2018 [arXiv:1807.07244 ]

• Golden Window (2010), Mathematics Magazine, 83 (5) 2010, no. 5, pp. 228-237.   
  (This is a creative contribution, recreational mathematics) 

2. Apollonian tangency spinors

Introduced here: 

• Clifford algebras and Euclid's parameterization of Pythagorean triples, 
  Advances in Applied Clifford Algebras (Mathematical Structures), 17 2007 pp. 71-93. 
  [arXiv:1201.4418]

For the more detailed exposition and the main theorems and properties, see: 

• Spinors and the Descartes configuration of circles 
  [arXiv:1909.06994]  (2019, 21 pages)

Further development and various applications:

• Integral spinors, Apollonian disk packings, and Descartes groups
  [arXiv:2105.12950]    (2021, 31 pages)
  
  
• Apollonian depth, spinors, and the super-Dedekind tessellation 
  [arXiv:2009.02680] (2020, 20 pages)
  

• Spinors, lattices, and classification of integral Apollonian disk packings,
  [arXiv:2001.05866] (2020, 35 pages)
  

• Tessellations and Descartes disk configurations 
  [arXiv:1910.05919 ]  (2019, 12 pages)

• Apollonian coronas and a new Zeta function
  [arXiv:1909.09941]  (2019, 19 pages)