May 11th, 2013, 11:33 AM  #1 
Newbie Joined: Dec 2012 Posts: 13 Thanks: 0  metric space Isometry
Notes: and the metric riemannian g at any point (x,y) is given by 
May 11th, 2013, 11:42 AM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: metric space Isometry
Does the map work?

May 11th, 2013, 11:58 AM  #3 
Newbie Joined: Dec 2012 Posts: 13 Thanks: 0  Re: metric space Isometry
How did you find that map?

May 11th, 2013, 12:04 PM  #4 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: metric space Isometry
It's an inversion about the circle . It's the only map that I know of that preserves the points on the circle but is not the identity. Basically, an inversion takes points outside the circle and puts them inside the circle, and takes points inside the circle and puts them outside the circle. It also preserves angles from the origin. The distance (calculated the normal way) from any point to the origin before the transformation is r, and after the transformation is .


Tags 
isometry, metric, space 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Discrete subgroups of isometry group of euclidean space  bigli  Real Analysis  0  November 23rd, 2013 04:30 AM 
Metric space  sebaflores  Real Analysis  2  September 30th, 2013 01:45 PM 
Metric Space  Fernando  Linear Algebra  0  November 29th, 2012 07:42 AM 
metric space  mathrookie2012  Real Analysis  4  January 22nd, 2012 02:27 AM 
metric space  mathrookie2012  Real Analysis  4  January 18th, 2012 06:10 PM 