The action of the M¨obius group on a circle is equivalent to the action of the linear fractional group on a projective line, if the circle is identified with the line by a stereographic projection. This implies the following.
The action of the M¨obius group on a circle is equivalent to the action of the linearfractional group on a projective line, if the circle is identified with the line by astereographic projection. This implies the following.