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Nov 23, 2014 at 9:52 comment added Rob lol. Yes you are right.
Nov 23, 2014 at 9:51 history edited Rob CC BY-SA 3.0
edited body
Nov 23, 2014 at 3:24 comment added KConrad You mean "fleshed out," not "flushed out."
Nov 23, 2014 at 0:56 comment added Hao Chen I finally got my own proof complete, and propose a fix to your proof, see my revised answer.
Nov 22, 2014 at 23:37 comment added Hao Chen Nah, I'm not ... see my answer.
Nov 22, 2014 at 22:50 comment added Hao Chen Sorry, I'm now OK with your proof.
Nov 22, 2014 at 21:36 comment added Hao Chen I'm not saying that the proof is wrong. But this is a detail that bothers me.
Nov 22, 2014 at 21:22 comment added Hao Chen In your picture, P is not the closest to l. There are closer points on the other side, for example (1, 1). By symmetry, (-1, -1) is a closer point below l with larger angle (or not depending on your meaning by angle).
Nov 22, 2014 at 21:16 comment added Rob You mean in the lower half plane? By symmetry, $(n,m) \in \mathbb{Z}^2$ is a minimizer of the orthogonal distance to $\ell$ iff $(-n,-m)$ is. Therefore it suffices to consider the upper half plane.
Nov 22, 2014 at 21:11 comment added Hao Chen What about the area between the parallel lines OQ and PR, with m<0 ?
Nov 22, 2014 at 20:44 history edited Rob CC BY-SA 3.0
added 265 characters in body
Nov 22, 2014 at 20:14 history edited Rob CC BY-SA 3.0
added 24 characters in body
Nov 22, 2014 at 20:03 history answered Rob CC BY-SA 3.0