Anjruu Posted July 24, 2005 Share Posted July 24, 2005 e^(i*pi)+1=0. What is it used for? Why is it special? Ok, it relates pi,e, i, 1, and 0, but does it have a practical application? Link to comment Share on other sites More sharing options...
□h=-16πT Posted July 24, 2005 Share Posted July 24, 2005 No, not really. Link to comment Share on other sites More sharing options...
matt grime Posted July 24, 2005 Share Posted July 24, 2005 Define practical. Why should it be practical? Maths is more than its mere applcitaions just as English is more than a mere language to communicate the fact that we want food. But the point was that it in one simple line links the most important mathematical objects there are. it doesn't need a practical application anymore than the Mona Lisa. You are entitled not to find it interesting or beautiful, but it is certainly succinct not to say elegant. Link to comment Share on other sites More sharing options...
Yggdrasil Posted July 24, 2005 Share Posted July 24, 2005 Euler's identity is used a lot in solving differential equations. It is also useful because it allows one to express the trigonometric functions in terms of exponential functions. Link to comment Share on other sites More sharing options...
Dave Posted July 24, 2005 Share Posted July 24, 2005 I think you're talking about the equation that the Euler identity is grabbed from: [math]e^{i\theta} = \cos\theta + i \sin\theta[/math] Link to comment Share on other sites More sharing options...
Yggdrasil Posted July 24, 2005 Share Posted July 24, 2005 My bad. Link to comment Share on other sites More sharing options...
Dave Posted July 24, 2005 Share Posted July 24, 2005 Not a problem. Just in case it isn't obvious for anyone, put [imath]\theta = \pi[/imath] into that equation, and Euler's identity will drop out. Link to comment Share on other sites More sharing options...
ydoaPs Posted July 24, 2005 Share Posted July 24, 2005 it also is an easy way to find the natural log of -1...[imath]\ln{-1}=i\pi[/imath] Link to comment Share on other sites More sharing options...
Tom Mattson Posted July 24, 2005 Share Posted July 24, 2005 e^(i*pi)+1=0. What is it used for? Why is it special? Ok, it relates pi,e, i, 1, and 0, but does it have a practical application? Take the more general version cited by dave, and yes it has numerous practical applications, by virtue of the fact that exponential functions are easier to calculate with than trigonometric functions. One very important application of complex exponentials is in electric circuit analysis in the frequency domain. Link to comment Share on other sites More sharing options...
Dave Posted July 24, 2005 Share Posted July 24, 2005 it also is an easy way to find the natural log of -1...[imath']\ln{-1}=i\pi[/imath] Whilst this is a bit offtopic, I should point out that it's not quite as simple as this. The above statement is certainly true; however, it can be expanded upon. You should be able to see that [imath]e^{(2n+1)i\pi} = -1[/imath] for [imath]n \in \mathbb{Z}[/imath], since [imath](-1)^{2n+1} = -1[/imath]. So you can quite easily say that [imath]\log(-1) = (2n+1)i\pi[/imath]. There's quite a nice little article about this at Dr. Math that I found from a quick google. I suggest people check it out, since it's rather informative Link to comment Share on other sites More sharing options...
Ollie Posted July 28, 2005 Share Posted July 28, 2005 e^(i*pi)+1=0. What is it used for? Historically, the best use of that line is to get annoying philosophers to shut up. Link to comment Share on other sites More sharing options...
DV8 2XL Posted July 29, 2005 Share Posted July 29, 2005 It's a stunningly beautiful relationship; what else does it need to be? Link to comment Share on other sites More sharing options...
Anjruu Posted July 29, 2005 Author Share Posted July 29, 2005 Nothing. I have only known it has a beautiful relationship, I was curious if there was more to it. Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now