My Math Forum How do you show a Möbius transformation maps circles to circles and lines?

 Geometry Geometry Math Forum

 November 3rd, 2015, 02:43 PM #1 Newbie   Joined: Nov 2015 From: UK Posts: 1 Thanks: 0 How do you show a Möbius transformation maps circles to circles and lines? So I have been trying to prove this for a week now. It is driving me crazy So the general equation of a circle is : (x-a)^2 + (y-b)^2= r^2 and you put that in the form zz ̅ – (z+z ̅) α + (z-z ̅ )αi = r^2- |α|^2 which in the w-plane is 1/(ww ̅ ) - ((w ̅+w)/(ww ̅ ))α + ( (w ̅-w)/(ww ̅ )) αi = r^2- |α|^2 now if the centre α = o - how do you prove that it maps to a line? Last edited by skipjack; November 3rd, 2015 at 03:16 PM.

 Tags circles, hod, lines, maps, möbius, mobius, show, transformation

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post justusphung Algebra 5 April 20th, 2013 10:30 AM RiDo Algebra 2 June 21st, 2012 01:31 AM aaron-math Calculus 1 October 19th, 2011 01:41 AM mbradar2 Calculus 2 November 2nd, 2010 06:28 PM greg1313 Algebra 2 May 31st, 2010 12:05 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top