Wolfram Cloud: Circle Inversion of "Interstitial Circles" on a Honeycomb Lattice скачать в хорошем качестве

Wolfram Cloud: Circle Inversion of "Interstitial Circles" on a Honeycomb Lattice

We use Wolfram Cloud (Mathematica) and the process of circle inversion to determine the radius of a certain circle. If six "kissing" circles surround the interior of a unit circle, those circles have a radius of 1/3. The question arose as to what was the radius of an "interstitial circle" that kissed two of these circles and the original unit circle. The problem was tackled using circle inversion of circles inscribed in a honeycomb lattice. It was easy to determine all the desired parameters (centers and radii) of the "honeycomb interstitials" and then employ circle inversion to determine the circles in the original problem. The radius was (5 - 2* sqrt(3))/13 which is approx. 0.118 which is a little more than 1/9.