The Sylvester–Gallai Theorem

(futilitycloset.com)

23 points | by surprisetalk 6 days ago

2 comments

  • hyperhello 10 minutes ago
    > Every finite set of points in the Euclidean plane that is not collinear has a line that passes through exactly two of the points.

    I can't make out the point here (no pun). Of course a line can pass through any two points. It could pass through three if those points were collinear but the statement says they're not. So what is the new fact?

    • math_loser 3 minutes ago
      > So what is the new fact?

      For all arbitrarily sized (but finite) sets of not collinear points, there's always a line that passes through exactly two points in the set.

    • chenb4425 5 minutes ago
      It’s that the line passes through exactly two points, which if you think about it is not exactly obvious.
  • emil-lp 53 minutes ago
    Futility closet is fantastic!