Hi,
Deron Stewart <deron@direct.ca>:
<<
You gotta like that "exp(i PI) = -1" thing, though.
That was a work of art. :)
>>
True. Even the proof of that is a work of art. If only all mathematics could be as pretty as that. One of the buildings here at Queensu campus has that formula etched into the stone work over the entrance.
One of the funniest mathematical texts I have ever read was the intro to my complex course textbook, where the author (foolishly) tries to rationalize the introduction of complex numbers ( i = squareroot(-1) ). He claimed that imaginary numbers are no more "radical" a modification to the number system than the jump from integers to reals was. Ha! I'm more inclined to view imaginary numbers are just that -- imaginary; a tool we use to help simplify the math. What is remarkable is how much it does simplify the math (just the concept of a transform alone makes them worthwhile, not to mention complex integration techniques and phasers...) But really, what is the square root of negative one?