This is not my area of research at all, but I think it’s super cool. The first time I heard of Apollonian circle packings was at that conference I went to in Marseille last month, during the first lecture of Hee Oh’s minicourse. So here’s a quick write up background of the first third of that lecture.
These packings and all this theory come from one dude, Apollonius of Perga, who wrote a bunch of math books back around 200 BC. Literally this math has been around for 2200 years. Here’s a paper submitted a month ago which is a generalization of Apollonius’s problem from circles to spheres. Math is so amazing! We live in history!
To understand the problem, we’ll have to do a quick geometry brush up. We say that two shapes or curves or lines in the plane are tangent if they touch at exactly…
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