rm: graph

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?

Gargoyle Gecko Owners

Last year I had decided to make a research paper on gargoyle geckos and had asked for measurements of your gargs. I ended up not having the time to do it but now I’m working on it again. Also, I have about 900 more followers than I did back then so I’m hoping some of you could help.
I’d like the age, weight, and length (or just age and weight) of your gargoyles
Preferably I’d have several measurements for each garg over time but that’s unlikely. I can’t use Lapillus because I don’t know for sure how old she is, though I ~think~ she’s going to be 2 in June. Not all gargs grow at the same rate, some can still be very very small for a long time while others grow fast but I’d like to have this graph in anyway. I’m not sure how long it will take to make this paper or how long I will make it but I am determined to do it now that I have the time again.
@kaijutegu, @kittje, @followthebluebell, @oriandico