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Circle in the Euclidean space using Euler's Number

  1. Aug 29, 2015 #1
    0 to 1 in Euclidean space.

    (1 + 1/n)^n using Euler's Number.

    1 to 0 with the circle.

    How amazing is Euler's Number?!
  2. jcsd
  3. Aug 29, 2015 #2


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    But welcome to PF!
  4. Aug 30, 2015 #3


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    What do you mean by "0 to 1 in Euclidean space"? What is changing from 0 to 1?

    What do you mean by "(1+ 1/n)^n using Euler's number"? Yes, the limit, as n goes to infinity is Euler's number but I would not say "with" Euler's number.

    And, finally, what do you mean by "1 to 0 with the circle"? What is changing from 1 to 0 and what does that have to do with the circle?
  5. Aug 30, 2015 #4
    I'm so confused by this post. Are you talking about how ##e^{i\theta}## is a circle in the complex plane with radius ##1##, or how the series expansion for ##(1+\frac{1}{n})^n## is ##e-\frac{e}{2n}+O(\frac{1}{n^2})##, or something else?

    Regardless, e certainly is an amazing number and pops up in tons of (un)expected places.
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