Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

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

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

Posts: 546
Registered: 12/6/04
Re: Cross Ratio of Four Concurrent Lines
Posted: Jun 30, 2013 4:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply
Xratio.jpg (67.1 K)

> Cross Ratio can be defined in projective geometry
> either for 4 collinear points or 4 concurrent lines.
> Point P connects 4 fixed points in x-y plane. Find
> locus of P so that cross ratio of the four ray pencil
> is a positive constant.
> Regards
> Narasimham

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


The result is shown in the attachment.

Best regards,

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

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.