June 20, 2010

e to the i times pi

I guess the order of the exponents in Euler's famous identity doesn't matter, so that e to the italicized i times pi arrives at the same terminus as e to the pi times italicised i, which is another way of ordering those three fundamental mathematical objects, e, pi, and italicized i, when going on about the profound interrelation of those objects arrayed just so that resolves itself inexorably at long last into a confirmation that the mathematical value we call "minus one" actually exists, is, in fact, identical to the very same thing pointed to by those mathematical objects when so arrayed. And if minus one exists, well, there you are. All the rest of the numbers can be reached from that simple unit that we, QED, don't have one of.

Salman Khan of the invaluable Khan Academy wends his way toward a demonstration of the circuitous and lovely math involved here and here.

1 comment:

rampster said...

HE HAD ME goin right up to the punchline when he seemed to choke on something which I can only imagine to be words.