http://www.mckeeth.org/2007/06/e-to-the-pi-times-i/ Jim McKeeth's blog about everything else Fri, 18 Jun 2010 05:00:07 -0400 http://wordpress.org/?v=2.8.6 hourly 1 http://www.mckeeth.org/2007/06/e-to-the-pi-times-i/comment-page-1/#comment-61688 ActualRandy Thu, 05 Feb 2009 06:57:02 +0000 http://www.mckeeth.org/2007/06/e-to-the-pi-times-i/#comment-61688 I wasn't familiar with that equation either, and I have a BS in math! But there are a ton of topics in math, and I only was exposed to some of them. Since Euler's Identity is part of algebra, and I never took non-abstract algebra in college, it never came up. Looks cool - thanks! I wasn’t familiar with that equation either, and I have a BS in math! But there are a ton of topics in math, and I only was exposed to some of them. Since Euler’s Identity is part of algebra, and I never took non-abstract algebra in college, it never came up. Looks cool – thanks!

]]> http://www.mckeeth.org/2007/06/e-to-the-pi-times-i/comment-page-1/#comment-61686 Juan Thu, 01 Jan 2009 19:38:05 +0000 http://www.mckeeth.org/2007/06/e-to-the-pi-times-i/#comment-61686 I also was perplexed at first with this beautiful identity. To understand it first you have to understand the Euler first derived e^(xi)= cos(x) isin(x). He arrived at this by using the accepted taylor polynomial for e^x= 1 x x^(2)/(2!) x^(3)/3! x^(4)/4 and so on. So, being as confident in his abilities as he was, Euler simply let x = xi. Then, as you probably noticed now, he let x = pi and got the extraordinary definition. I also was perplexed at first with this beautiful identity. To understand it first you have to understand the Euler first derived e^(xi)= cos(x) isin(x).
He arrived at this by using the accepted taylor polynomial for e^x= 1 x x^(2)/(2!) x^(3)/3! x^(4)/4 and so on. So, being as confident in his abilities as he was, Euler simply let x = xi. Then, as you probably noticed now, he let x = pi and got the extraordinary definition.

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