Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Rob Johnson Posts: 1,771 Registered: 12/6/04
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.pledger-5C6734.16302428072011@news.eternal-september.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

Date Subject Author
7/27/11 Vivian DeRoth
7/27/11 Rob Johnson
7/28/11 Ken.Pledger@vuw.ac.nz
7/28/11 Rob Johnson
7/28/11 Vivian DeRoth
7/28/11 Ken.Pledger@vuw.ac.nz
7/28/11 Rob Johnson