20 citations · 84 across the 35 of their papers we have counts for
7 papers · 1 filter
Apollonian depth, spinors, and the super-Dedekind tessellation
Jerzy Kocik
The configuration space of tricycles (triples of disks in contact) is shown to coincide with the complex plane resulting as a projective space costructed from the tangency and Paul…
Induced orders in free monoids of words
Jerzy Kocik
A family of partial orders in the free monoid of words, induced from a partial order in alphabet, is presented. The induced orders generalize the chronological posets that have bee…
On a Diophantine equation that generates all integral Apollonian Gaskets
Jerzy Kocik
A remarkably simple Diophantine quadratic equation is known to generate all Apollonian integral gaskets (disk packings). A new derivation of this formula is presented here based on…
Traces, symmetric functions, and a raising operator
Jerzy Kocik
The polynomial relationship between elementary symmetric functions (Cauchy enumeration formula) is formulated via a ``raising operator" and Fock space construction. A simple graphi…
Fibonacci numbers and Ford circles
Jerzy Kocik
An amusing connection between Ford circles, Fibonacci numbers, and golden ratio is shown. Namely, certain tangency points of Ford circles are concyclic and involve Fibonacci number…
Apollonian depth and the accidental fractal
Jerzy Kocik
The depth function of three numbers representing curvatures of three mutually tangent circles is introduced. Its 2D plot leads to a partition of the moduli space of the triples of…