Thread: moebius, poincare model/complex numbers

imagine a semi circle (x-2)+y^2=2 so centre (2,0) and radius 2 for the upper half plane,
call the semi circle p.

I need to give the formula for the reflection across p (hyperbolic reflection)

i then have points S=4+3i for example where i need to find i can make stabby attempts but half the other questions depend on getting the correct formula for .

thanks,,v desperate.

Originally Posted by skystar

imagine a semi circle (x-2)+y^2=2 so centre (2,0) and radius 2 for the upper half plane,
call the semi circle p.

I need to give the formula for the reflection across p (hyperbolic reflection)

i then have points S=4+3i for example where i need to find i can make stabby attempts but half the other questions depend on getting the correct formula for .

thanks,,v desperate.

The semi-circle would be if it had a radius of 2. What is the definition of the hyperbolic reflection ?

A hyperbolic reflection in the Poincare Half-Plane is an inversion. If we choose to think of the upper half plane as the complex plane then inversions are actually Mobius transformations.

sorry excuse my lame example
a hyperbolic function R as a function of z is
and is given by as a general result.k is constant, r is radius
if i sub in 2 for both k and r then i can reduce it easily but this is not