https://www.youtube.com/watch?v=u-_vr7cPUtA

I wanted to know how to specify and create all possible Steiner chains in the extended complex plane.
This was made much easier by the fact that Steiner chains are closed under mobius transformations.

I wrote the code in R, rendered it to .png using Cairo, and then converted to .mp4 with ffmpeg.

I used these sources heavily while putting this together:

[1] Pedoe, D. (1970) Geometry, a Comprehensive Course, Cambridge University Press, Cambridge.

[2] https://en.wikipedia.org/wiki/Steiner_chain

[3] https://en.wikipedia.org/wiki/Generalised_circle

[4] https://en.wikipedia.org/wiki/M%C3%B6bius_transformation

#steinerchains #steinersporism #mobius #mobiustransforms