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Topic: Cross Ratio of Four Concurrent Lines
Replies: 6   Last Post: Jul 9, 2013 11:29 AM

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 Narasimham Posts: 356 Registered: 9/16/06
Re: Cross Ratio of Four Concurrent Lines
Posted: Jul 1, 2013 3:33 PM

> Hi Narasimham,
>
> the problem is very interesting. I studied the
> special case A=[1 0], B=[0 1], C=[-1 0], D=[0 -1],
> where point P is element of the box [-2 2]x[-2 2],
> and tet=angle(APB), phi=angle(BPC), psi=angle(CPD).
> For the Cross Ratio we have
>
> CR=sin(tet+phi)*sin(phi+psi)/(sin(tet+phi+psi)*sin(phi
> )).
>
> The result is shown in the attachment.
>
> Best regards,
> Avni

Hi Avni,

May be you like to sketch a few line loci inside the red area for some particular CR values.

Best Regards,
Narasimham

Date Subject Author
6/28/13 Narasimham
6/30/13 Avni Pllana
7/1/13 Narasimham
7/1/13 Avni Pllana
7/1/13 Avni Pllana
7/9/13 Narasimham
7/7/13 Narasimham