I always wondering about the use of square pixels over triangular ones. Maybe more of an engineering problem than a math problem, but would be interesting to see how triangular pixels deal with antialiasing better. Though there may be other problems I am forgetting.
If thinking about the details of real screens in previous slide, the pixels obvious are not square. We call it "square" only for simplify problem in my understanding.
Referencing an above comment, are pixels even actually squares these days? It seems to me like they are point light sources that are arranged in rows and columns perfectly horizontally and vertically. This gives them the appearance of squares because the space they occupy is square, but we really see this exaggerated square-ishness on the right when we zoom in such that multiple pixels in a squared shape are made to represent one pixel.
The geometry of the pixels is sometime taken into account for anti-aliasing. This is called subpixel rendering. It is often used for rendering text. https://en.wikipedia.org/wiki/Subpixel_rendering