course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Geometry |
IB |
27 |
|
Paper 2, Section II, G |
2009 |
What is meant by stereographic projection from the unit sphere in
Derive an explicit formula for stereographic projection. Hence, or otherwise, prove that if a Möbius map corresponds via stereographic projection to a rotation of the sphere, it has two fixed points
(i) a Möbius transformation which fixes a pair of points
(ii) an isometry of the sphere (for the spherical metric) which does not correspond to any Möbius transformation under stereographic projection.