0
$\begingroup$

Can someone describe the circle group $S^1$ in a easily understandable way? Are elements in $S^1$ in the form of $e^{2i\theta\pi}$? What does this look like pictorially? Doesn't necessarily need a graph but maybe at least describe it? Appreciated!

$\endgroup$
  • 1
    $\begingroup$ It's... a circle. The group operation is multiplication like you describe. I'm not quite sure what your question is asking. Do you know that complex numbers have that representation, and that $e$ to an imaginary power is norm 1? $\endgroup$ – Alfred Yerger Apr 16 at 2:53
  • $\begingroup$ I guess I'm not sure about e to an imaginary number power. I will look into that, thank you $\endgroup$ – yyyy Apr 16 at 3:00
  • $\begingroup$ Instead of considering elements of the group as $e$ to an imaginary power, simply consider them to be angles. Then the group operation is addition of angles. $\endgroup$ – Solomonoff's Secret Apr 16 at 3:04
  • $\begingroup$ Oooooor consider them to be the real numbers modulo $1$, or modulo $2\pi$. Or rigid rotations of a circle. Pictorically it's just a circle. $\endgroup$ – Jackozee Hakkiuz Apr 16 at 3:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.