Wednesday, 17 August 2011
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...