1. ## Pi Versus e

Can e^(pi) be calculated? What about pi^(e)? Is this important in any way?

2. ## Re: Pi Versus e

Originally Posted by harpazo
Can e^(pi) be calculated? What about pi^(e)? Is this important in any way?
Get your calculator out and find the $\displaystyle x^y$ key. Then hit $\displaystyle \pi ~ x^y ~ e$.

As to a use I don't know of anything. However $\displaystyle e^{i \pi} = -1$ is a very useful relation.

-Dan

3. ## Re: Pi Versus e

Originally Posted by topsquark
Get your calculator out and find the $\displaystyle x^y$ key. Then hit $\displaystyle \pi ~ x^y ~ e$.

As to a use I don't know of anything. However $\displaystyle e^{i \pi} = -1$ is a very useful relation.

-Dan
What level of math uses the equation you posted? Why is that equation important?

4. ## Re: Pi Versus e

Since e^(i•pi) = -1, can it be said that e^(i•pi) = i^2 as well?

5. ## Re: Pi Versus e

Originally Posted by harpazo
Since e^(i•pi) = -1, can it be said that e^(i•pi) = i^2 as well?
True but it's usefulness is contained in what's called Euler's identity $\displaystyle e^{i \theta } = cos( \theta ) + i~sin( \theta )$ in conjuction with de Moivre's theorem: $\displaystyle (cos( \theta ) + i~sin( \theta ) )^n = cos( n \theta ) + i~ sin( n \theta )$. This has all sorts of uses in Geometry and (what I know best) Physics where complex numbers are used. Many properties in Physics have some sort of "attenuation" properties and complex numbers can often be used to describe the phenomena. These identities make it easy to introduce such.

-Dan

6. ## Re: Pi Versus e

Originally Posted by topsquark
True but it's usefulness is contained in what's called Euler's identity $\displaystyle e^{i \theta } = cos( \theta ) + i~sin( \theta )$ in conjuction with de Moivre's theorem: $\displaystyle (cos( \theta ) + i~sin( \theta ) )^n = cos( n \theta ) + i~ sin( n \theta )$. This has all sorts of uses in Geometry and (what I know best) Physics where complex numbers are used. Many properties in Physics have some sort of "attenuation" properties and complex numbers can often be used to describe the phenomena. These identities make it easy to introduce such.

-Dan
I am obviously far away from advanced topics but good to know it's there for me to explore in the future (if life allows).