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Topic:
Inverse of a conic with regard to the centre is an oval of Cassini
Replies:
6
Last Post:
Jul 28, 2011 7:33 AM




Re: Inverse of a conic with regard to the centre is an oval of Cassini
Posted:
Jul 28, 2011 1:33 AM


In article <ken.pledger5C6734.16302428072011@news.eternalseptember.org>, Ken Pledger <ken.pledger@vuw.ac.nz> wrote: >In article <20110727.164137@whim.org>, Rob Johnson <rob@trash.whim.org> >wrote: > >> .... >> If we invert the points (x > x/r^2, y > y/r^2) .... > > >x > (r^2)/x, y > (r^2)/y ?
The direction is preserved, but the distance is inverted. That means x > x/r^2 and y > y/r^2. This is made explicit in
<http://en.wikipedia.org/wiki/Inversive_geometry#Inversion_in_higher_dimensions>
I have used a radius of 1 since inversions with different radii are simply dilations of each other.
You can also check Section 2 of
<http://www.whim.org/nebula/math/pdf/inversion.pdf>
Rob Johnson <rob@trash.whim.org> take out the trash before replying to view any ASCII art, display article in a monospaced font



