# Circle in the Euclidean space using Euler's Number

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?!

Mentallic
Homework Helper
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?!
What...?

But welcome to PF!

HallsofIvy
Homework Helper
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?

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.