Reminds me of flatland: There are three circular buildings. There's a line that all three people can be on such that each person thinks there are only two buildings and no one can agree on which two buildings are present.

Edit: Nope, nevermind, two of the points both see the medium and small circles!

Is this the start of a new approach to public-key cryptography?

The wikipedia page has mostly geometric proofs. Are there algebraic proofs?