cancel
Showing results for 
Show  only  | Search instead for 
Did you mean: 
JMP is taking Discovery online, April 16 and 18. Register today and join us for interactive sessions featuring popular presentation topics, networking, and discussions with the experts.
Choose Language Hide Translation Bar
Craige_Hales
Super User
Kissing Circles

JSL, attached below, creates a set of still frames in a directory on the desktop that can be combined to make this video. There are a lot of sites describing Soddy Circles, Kissing Circles, Apollonian Gaskets, and Descartes' Theorem. The first link has a poem too, which includes all the math. The short story: in two dimensions, four circles can all touch each other, and there is a simple relationship between their sizes. And, for any three of the four, there is another circle that will make different set of four.

To make this video, I used a zero-to-two-PI sin and cos function to vary the sizes of the seed circles, and to rotate the image. The final frame is the same as the first. The circle at 3-o'clock in the initial frame is the one to observe if you are trying to figure out what is going on.

Update 4 Feb 2017: repair formatting for new community.

Last Modified: Feb 4, 2017 8:31 AM
Comments