general topology - Why do we denote $S^1$ for the the unit …
Students look at a circle as a $2$-D shape geometrically, and then don't get that topologically it can be described with a single parameter. $\endgroup$ – rschwieb Commented Jul 3, 2014 at 15:34
Homeomorphism and Unit circle - Mathematics Stack Exchange
Dec 27, 2019 · An injective continuous self-map of the unit circle is a homeomorphism. 0.
How do you evaluate #arcsin(1/2)#? - Socratic
Jun 9, 2015 · Trig unit circle gives another arc x that has the same sin value (1/2): x = (180 - 30) = 150 deg. Answer ...
How do I get the slope on a circle? - Mathematics Stack Exchange
I have drawn a circle by doing this in Matlab: syms x; ezplot(cos(x),sin(x)) I get the tangent point at ...
general topology - The unit interval homeomorphic to the unit …
The unit interval homeomorphic to the unit circle. Ask Question Asked 4 years, 1 month ago. Modified 1 ...
How does $e^{i x}$ produce rotation around the imaginary unit …
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general topology - $S^1$ is not homeomorphic to an interval ...
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Show that unit circle is not homeomorphic to the real line
May 12, 2018 · Another argument is that removing a single point from a circle leaves a connected space, while that is not true of $\mathbb{R}$. $\endgroup$ – user296602 Commented May 12, 2018 at 16:41
calculus - Prove that the unit circle is path-connected?
For proving that the unit circle is connected, you could also say that "the only subsets of the unit circle which are both open and closed are the full circle and the empty set". Which is obvious when you think about it.
Area of circle (double integral and cartesian coordinates)?
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