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Archived: 07 Aug 2014, 09:47
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bonzo
Joined: 01 Aug 2009, 17:36 Posts: 2
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 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: http://www.roadsolutions.ox.ac.uk/solut ... ution2.jpgCan 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!
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01 Aug 2009, 17:44 |
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vasco
Supporter
Joined: 07 Jun 2008, 08:21 Posts: 235
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 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 
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02 Aug 2009, 06:53 |
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DimBulb
Joined: 07 May 2009, 16:45 Posts: 62
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 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 
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02 Aug 2009, 07:20 |
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bonzo
Joined: 01 Aug 2009, 17:36 Posts: 2
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 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 :)))))))))))
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02 Aug 2009, 09:14 |
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