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Exercise [02.04]
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Joined: 01 Aug 2009, 17:36
Posts: 2
Exercise [02.04]
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:

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.

01 Aug 2009, 17:44
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Joined: 07 Jun 2008, 08:21
Posts: 235
Re: Exercise [02.04]
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

02 Aug 2009, 06:53

Joined: 07 May 2009, 16:45
Posts: 62
Re: Exercise [02.04]
Maybe your confusion stems from not realizing that two letters here is a positive distance. So is the distance from point to point

02 Aug 2009, 07:20

Joined: 01 Aug 2009, 17:36
Posts: 2
Re: Exercise [02.04]
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 :)))))))))))

02 Aug 2009, 09:14
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