Circle packing theorem

Recently I heard about this surprising theorem. I already knew about Fáry’s theorem: if a simple graph can be drawn on the plane without crossing edges (i.e. if the graph is planar), then it can always be drawn in such a way that all edges are non-crossing straight lines. Hence, restricting to straight-line edges doesn’t give a strictly smaller class of planar graphs. I found this to be quite surprising already.

However, much more is true: you can always draw a simple planar graph in the plane in such a way that you can place non-overlapping circles on the vertices, such that two circles touch if and only if the corresponding vertices are joined by an edge. In particular, the drawing clearly satisfies the result of Fáry’s theorem. This result is called the circle packing theorem.

5.16.17 | 8:46pm | 3/100 days of productivity

finals are coming up soon (for me they’re the week of may 29) so i’ve been studying all the math i’ve learned this year, one topic at a time. today: parent functions!

also should i make a calligraphy tips post? i feel like a lot of the people in this community are trying to learn it for notes + bujo spreads, and i’ve been doing calligraphy for years and only recently added it to my schoolwork. so what do you think? should i make a post about it?