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Topic: point of symmetry (Read 8100 times) 

trusure
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point of symmetry
« on: Apr 20^{th}, 2009, 5:19pm » 
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while I was trying to find a Linear Fractional Transformation from the upper half plane to itself, with 0 mapped to 1 and i mapped to 2i, I used that the point of symmetric of i is i mapped to 2i which is the point of symmetric for 2i,(using the symmetric principle), so now I have 3 pints mapped to 3 points, and using the cross ratio I found f(z)=2.5 *z +1 ! which is not correct ?? so, where is my mistake ?? can anyone help me ? Thank you

« Last Edit: Apr 20^{th}, 2009, 5:20pm by trusure » 
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Eigenray
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Re: point of symmetry
« Reply #1 on: Apr 20^{th}, 2009, 8:11pm » 
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Probably not, if you don't show what you did. Solving (z, 0; i, i) = (f(z), 1; 2i, 2i) for f(z) should work.


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trusure
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Re: point of symmetry
« Reply #2 on: Apr 20^{th}, 2009, 8:56pm » 
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does it matter the order of the points while using the cross ratio ?!!

« Last Edit: Apr 20^{th}, 2009, 9:17pm by trusure » 
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Eigenray
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Re: point of symmetry
« Reply #3 on: Apr 20^{th}, 2009, 9:26pm » 
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No, as long as you put the points in the same order as their images. E.g., (i, 0; z, i) = (2i, 1; f(z); 2i) would also work, but not (z, 0; i, i) = (f(z), 2i; 2i, 1)


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