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Math Forum » Discussions » Math Topics » geometry.puzzles.independent

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

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Avni Pllana

Posts: 503
Registered: 12/6/04
Re: Cross Ratio of Four Concurrent Lines
Posted: Jul 1, 2013 5:14 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
Xratio2.png (25.8 K)

> > 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

The figure in the attachment reveals the striking
beauty of CR. The values of CR greater than 2 or less than -2, are truncated to 2 and -2 respectively.

Best regards,
Avni

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