- How do you parameterize a circle? - Mathematics Stack Exchange
Your parametrization is correct Once you have a parameterization of the unit circle, it's pretty easy to parameterize any circle (or ellipse for that matter): What's a circle of radius $4$? Well, it's four times bigger than a circle of radius $1$!
- Can we characterize the Möbius transformations that maps the unit disk . . .
So the answer is that the Möbius transformations sending the unit circle to itself are precisely the Möbius transformations sending the unit disc to itself, and their multiplicative inverses
- How does e, or the exponential function, relate to rotation?
First, assume the Unit Circle Parameter is Time in Seconds The essential idea is that in order for a Radius of Length 1 to move 1 Arc Length in 1 Second it is required to have a Velocity of 1, Acceleration of 1, Jolt of 1, etc
- Show that unit circle is not homeomorphic to the real line
Show that unit circle is not homeomorphic to the real line Ask Question Asked 7 years, 6 months ago Modified 6 years, 2 months ago
- Möbius transformation mapping - Mathematics Stack Exchange
7 For your first example, because the boundary of the upper half-plane is a "circle" (in the Riemann sphere sense (sorry, Riemann sphere, not Bloch sphere)), and the boundary of the unit disk is a circle (plainly, but also in the Riemann sphere sense), we try to map the boundary of the one to the boundary of the other
- calculus - Trigonometric functions and the unit circle - Mathematics . . .
Since the circumference of the unit circle happens to be $ (2\pi)$, and since (in Analytical Geometry or Trigonometry) this translates to $ (360^\circ)$, students new to Calculus are taught about radians, which is a very confusing and ambiguous term
- How does $e^ {i x}$ produce rotation around the imaginary unit circle?
Time is point rotation in a circle There are 2 other circles and 2 other point rotations around those circles that are all mutually perpendicular to each other, therefore separate dimensions
- How do I get the slope on a circle? - Mathematics Stack Exchange
The prior answers have all used calculus I'm going to post an answer using only trig The following diagram from Wikipedia's Trig Page is helpful However, that diagram also has a fault--the picture is very cluttered :) Thus, I've redrawn it for you, labeling the components important for this problem: Note that $\csc\theta$ returns the distance from the origin to the y-intercept of the
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