
Re: Cross Ratio of Four Concurrent Lines
Posted:
Jul 1, 2013 5:14 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
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

