Why nobody is talking about how cool it is that he snaps his fingers to clean the board? As mathematics teacher I create my own videos as well and this gives me great ideas! Love this video.
Your channel is so good. It's wonderful to watch this more advanced stuff; it takes me back to my undergraduate days and all those happy memories. Best wishes to you from the UK.
This absolutely is the same for me. These video's take me back to my first years studying math at my uni and also it brings the joy of understanding the material better than back in those early years.
The drawings starting around 7:50, combining rotation and reflexion of an n-gon presuppose that n is odd. Strictly speaking you should check that the result is the same when n is even.
At 10:00, it should be n-1 clockwise rotations (r^n-1) followed by a reflection that fixes 1 (s) to be consistent. What you did was n-1 counter-clockwise rotations (r^(n-1))^(n-1), following by a reflection that fixes n (which is not s).
We must be careful not to confuse rotation as being restricted to it's common definition of rotating through 2pi or 360 degrees. In this context a rotation means a "motion." If not then writing that the number of rotations=2(pi) K/n where k is )=k-< or equal to n-1 is confusing. Example: Set n=3 (a triangle) we have that 2(pi) k/3- the number of rotations, implying K=9/2(pi) which is about 3/2( not even an integer in the set[0,N-1} . It's about one and a half rotations which certainly note equal to what is correct:3 .
