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Thread: Pi Versus e

  1. #1
    Super Member harpazo's Avatar
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    Pi Versus e

    Can e^(pi) be calculated? What about pi^(e)? Is this important in any way?
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    Forum Admin topsquark's Avatar
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    Re: Pi Versus e

    Quote Originally Posted by harpazo View Post
    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
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    Super Member harpazo's Avatar
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    Re: Pi Versus e

    Quote Originally Posted by topsquark View Post
    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?
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    Super Member harpazo's Avatar
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    Re: Pi Versus e

    Since e^(i•pi) = -1, can it be said that e^(i•pi) = i^2 as well?
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    Forum Admin topsquark's Avatar
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    Re: Pi Versus e

    Quote Originally Posted by harpazo View Post
    Since e^(ipi) = -1, can it be said that e^(ipi) = 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
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    Super Member harpazo's Avatar
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    Re: Pi Versus e

    Quote Originally Posted by topsquark View Post
    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).
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