Question

Here's a fun question.

Is there a set \(K\) in \(\mathbb R^2\) that intersects every line exactly twice?

Can you prove it?

Answer 1

(I know the answer already, it's just a cool problem)

Answer 2

http://mathoverflow.net/questions/21470/subset-of-the-plane-that-intersects-every-line-exactly-twice

Answer 3

Yep, that's pretty much the proof I had in mind :)