I have wanted to see this sort of thing working for sooooo long! Click the eyes, nose or mouth...

Edit: There's a nicer example I've done over at this blog

Edit 2. It seems broken at the moment. Will check back on this stuff...

Fermat's lost "proof"?

Google's Doodle today reminded me of some old thoughts. First, see this Explanation

Years ago I read Simon Singh's book on this & got scribbling after I imagined there could be a simple geometric proof rather than an algebraic one. A proof that Fermat could have seen.

Basically, a**n + b**n = c**n is solvable when n = 1 or 2, but not for 3 or more.

I saw these three formula elements as three LINES and thus -

Powers of 1 describe straight lines eg 1**1 + 2**1 = 3**1 with the the lines overlaying each other in a ONE dimensional space.

Powers of 2 described right angle triangles on a TWO dimensional space eg 3**2 + 4**2 = 5**2.

Powers of 3 however would describe three lines arranged into a THREE dimensional object, which CANNOT be done... the core of the possible proof.

Powers above 3 would face the same general restriction, ie we don't have enough lines to create the object with those dimensions.

Who knows? Maybe someone can tell me why this is a false line of reasoning, or...