Hacker News: chenb4425

New comment by chenb4425 in "The Sylvester–Gallai Theorem"

chenb4425 — Fri, 07 Aug 2026 15:13:14 +0000

That's only assuming your set of points only contains three points. If you have four or more points, it's entirely possible that a line you draw between two points passes through a third.

...

If you're given the above set of points, it's obviously not collinear due to the point at the top, but if you draw a line through any of the bottom two points, it will hit a third.

New comment by chenb4425 in "The Sylvester–Gallai Theorem"

chenb4425 — Fri, 07 Aug 2026 05:19:48 +0000

I think you are mistaking the fact that you can easily find an example satisfying the theorem’s statement with the proof that the statement is always true. Of course given any set of points that aren’t all on the same line, your nine your old could find a line passing through only two points. But could they explain to you why this is always possible, no matter the configuration of points? You can’t just say “I draw a line between two points and that’s it.” You must also explain why there isn’t a third point on the line, and why that line’s existence is guaranteed, which is not obvious (at least to me).

New comment by chenb4425 in "The Sylvester–Gallai Theorem"

chenb4425 — Fri, 07 Aug 2026 02:47:49 +0000

It’s that the line passes through exactly two points, which if you think about it is not exactly obvious.