I was reading the book Fermat's Last Theorem Simon Singh and in chapter 3 he mentions the "Dot Conjecture", and gives a proof in the appendix.
However, the "proof" seems to me as a just more elaborate way of stating that the proof is obvious and trivial. I was talking with a friend and she is also clueless. Furthermore, I couldn't even find any reference to it by googling. I realise that, since this is a pop-math book, he might not be using the "official" name of this conjecture.
If somebody could explain it to me or at least give some link or further reading, I'd be very grateful.
Taking back the proof from where it stops, imagine that there is a third point on that line (call it $ AB $ where $ A $ is on the left and $ B $ on the right, with $D$ the "closest point" below the line as per the picture's notation), if the third point, say $ C $ is on the left of the picture, then the distance from $ A $ to the line $ CD $ is shorter than the dashed segment. You get a similar contradiction if $ C $ is on the right, or between $ A $ and $ B $.