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trusure
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 point of symmetry   « on: Apr 20th, 2009, 5:19pm » Quote Modify

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 20th, 2009, 5:20pm by trusure » IP Logged
Eigenray
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 Re: point of symmetry   « Reply #1 on: Apr 20th, 2009, 8:11pm » Quote Modify

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 20th, 2009, 8:56pm » Quote Modify

does it matter the order of the points while using the cross ratio ?!!
 « Last Edit: Apr 20th, 2009, 9:17pm by trusure » IP Logged
Eigenray
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 Re: point of symmetry   « Reply #3 on: Apr 20th, 2009, 9:26pm » Quote Modify

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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