In the last lecture we had a look at tilings of the hyperbolic plane. We want to tile the plane with regular $p$-gons, such that at each vertex $q$ polygons meet. Then we do a little calculation and see that for $\frac1p+\frac1q < \frac12$ there exist such tilings of the hyperbolic plane.
These tilings can be generated by a software written by Martin von Gagern from TU Munich. It is written in Java and can be downloaded from his website. I created an Escher like picture with it 🙂
Sorry, but I didn’t find the time to blog the lectures so far but I scanned my notes. Sorry for the bad quality but I will try to improve it. But for the moment these are the available scans:
Lecture_26 Lecture_27 Lecture_28
Comment … I just printed one of the files and it looks terrible but somehow scanning pencil written notes is not as easy as I expected …
Lecture26 Lecture27 Lecture28
Now it’s much better – I hope 🙂
As I used various $\LaTeX$ commands and shortcuts which are not available here, I will not upload lectures 26 and 27 into the blog.
Yet they are included in the pdf version of the lecture notes which is available here.