Jump to content

stereographic projection on complex plane

Meital
in Analysis and Calculus

Featured Replies

Stereographic projection on complex plane

--------------------------------------------------------------------------------

Let V be a circle lying in S. Then there is a unique plane P in R^3 such that p /\ S = V ( /\ = intersection). Recall from analytuc geomerty that

P = { (x_1,x_2,x_3) : x_1 b_1 + x_2 b_2 + x_3 b_3 = L, where L is a real number}.

Where ( b_1,b_2,b_3) is a vector orthogonal to P . It can be assumed that (b_1)^2 + (b_2)^2 + (b_3)^2=1. Use this information to show that if V contains the point N then its seteographic projection on the complex plane is a straight line. Otherwise, V projects onto a circle in complex plane.

 

N = (0,0,1) the north pole on S

 

Please any hints will be appreciated!! :rolleyes:

Archived

This topic is now archived and is closed to further replies.

Go to topic listing

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.

Configure browser push notifications
Chrome (Android)
  1. Tap the lock icon next to the address bar.
  2. Tap Permissions → Notifications.
  3. Adjust your preference.
Chrome (Desktop)
  1. Click the padlock icon in the address bar.
  2. Select Site settings.
  3. Find Notifications and adjust your preference.