WARNING: PROJECTIVE GEOMETRY MAY PUT HOLES IN YOUR BRAIN. YOUR MIND MIGHT LEAK OUT - IF YOU WANT YOUR MIND IN YOUR BRAIN STOP READING NOW. Okay, here is a geometric exercise that I find very interesting (for some context about WHY it is interesting, look here). It is, however, more complicated than the previous one...
I'd like to make a contribution with regards to circularity/linearity, from a geometrical standpoint. If you don't like geometry, stop reading, or better yet, read with increased intensity. The polarity between circle/line is one that is fundamental to many geometries - they are taken to be quite different logical entities. Primarily this arises because of...