31–40 of 59 posts
e^ix = cos x + i sin x
Sadly, this article did nothing for me. I will remember to lookup wikipedia first...
Can anyone name some of the actual uses of this equation in solving real world problems?
Personally, I prefer e ^ i*tau = 1 But that's because I'm a tauist.
The advantage of the traditional format is that it not only includes four fundamental constants (1, 0, e, i and π) but it also includes the four fundamental operators (addition, multiplication, exponential and equality.) I guess that: e ^ i*tau + 0 = 1 would be a suitable hack to get that beauty back.
b^)
I wish I could take my up vote back. I read this article and the power series expansion of the exponential function was not clear. So I looked up the wikipedia article ( http://en.wikipedia.org/wiki/Exponential_function ) and http://en.wikipedia.org/wiki/Euler%27s_formula which were much more clearer. Sadly, this article did nothing for me. I will remember to lookup wikipedia first...
I would say that the Fundamental Theorem of Galois Theory is the most beautiful result of all mathematics, though Euler's identity is certainly a contender.
In actuality, this article has not provided any useful information, and especially not helped anyone truly 'understand the most beautiful equation in Mathematics'. However, if someone is looking for, in my opinion, a real explanation, I feel as though Kalid Azad's explanation of Euler's identity (http://betterexplained.com/articles/intuitive-understanding-...) is fairly thorough and insightful.
I would say that the Fundamental Theorem of Galois Theory is the most beautiful result of all mathematics, though Euler's identity is certainly a contender.
Could you suggest any resource for understanding this theorem? I have a math degree, but I never came across any Galois theory.
http://www.amazon.com/Abstract-Algebra-Edition-David-Dummit/...
When I learned it, though, it was from this Dover book, which is more affordable:
http://www.amazon.com/Elements-Abstract-Algebra-Dover-Mathem...
Can anyone name some of the actual uses of this equation in solving real world problems?
I think the actually remarkable equation is e^ix = cos x + i sin x The cliched "e^(i pi) + 1 = 0" is a fairly mundane consequence of the fact that pi was chosen to make this equation hold.