Hi all,
I was writing a solution for this problem and while checking if it was right I've found this one on Penrose's home page:

http://www.roadsolutions.ox.ac.uk/solut ... ution2.jpg

Can I kindly ask you why:
Mainly what's not so clear to me is the fraction , could you please explain me why this equation holds?

For those interested there's another published solution: http://downroadtoreality.blogspot.com/2 ... se-24.html that's IMHO more elegant than the first one, even if it's less clear.

Thanks for your help!

From the diagram given with the solution:

is similar to , since and .

So

Also from the diagram:



and



Dividing both sides of by and both sides of by gives:



and



Using (1) and substituting shows that the RHS of (4) and the RHS of (5) are equal and so

Maybe your confusion stems from not realizing that two letters here is a positive distance. So is the distance from point to point

Thank you vasco, I was puzzled because I didn't understand how he came up with the idea of dividing (2) by SP and (3) by OP (alas I didn't have the same idea when trying this kind of demonstration :().
Thank you so much again, everything is clear now :)))))))))))