Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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


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

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Avni Pllana

Posts: 477
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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.