# Questions tagged [stereographic-projections]

For question about stereographic projection, a particular mapping that projects a sphere onto a plane.

121 questions
1answer
13 views

1answer
166 views

1answer
42 views

### How to describe the relative positions?

There is a problem in my complex variable textbook as follows: Discribe the relative positions of the images of $z$, $-z$ and $\bar z$ on the Riemann sphere. But I don't understand what does this ...
2answers
45 views

1answer
2k views

### The inverse map of the stereographic projection

Let $\mathbb S^1$ the unit circle centered at the origin and the pole $p=(0,1)$. The stereographic projection is the homeomorphism $\varphi:\mathbb S^1\setminus \{p\}\to \mathbb R^1$. In order to find ...
1answer
348 views

### Projecting the line y=x onto the Riemann Sphere

I am trying to project the line "y=x" on the complex plane including the point at infinity to the Riemann Sphere. I know the projection is a circle, but I want to understand how to find the radius of ...
0answers
164 views

### 2 dimensional sphere

For $a,b,c >0$ let, $E(a,b,c) = \{ (x,y,z) \in \mathbb {R^3} : \frac {x^2}{a^2} +\frac {y^2}{b^2} + \frac {z^2}{c^2} =1 \}$ I am asked to Show that $E(a, b, c)$ is diffeomorphic to the 2-...