User blog comment:Plain'N'Simple/A cool geometric connection regarding the fast-growing-hierarchy/@comment-35470197-20191224012438/@comment-39541634-20191229161658

The log(2) one is a good pure example. The others have additional factors, so I don't really think they should count.

Speaking of log(2), it also has a nice geometrical meaning:

It is the area bounded by the hyperbola y=1/x and the lines x=1, x=2.

I'm too lazy at the moment to precisely translate the above sentence into a pure geometry problem, but it seems possible: Just describe the hyperbola as a locus and draw two parallel lines in the right place.