Mobius Transformation: Physical Significance?

[Layman FJ]

In Mobius geometry it is assumed that a line is a circle of infinite radius.Does this have any physical significance?

 

[Ssnow]

it is assumed that a line is a circle of infinite radius

Mobius transformations transform map every straight line to a line or circle, and map every circle to a line or circle. You obtain these transformations by stereographic projection from a plane to a sphere. In physics they form a group structure well know as $SL(2,\mathbb{C})$ and tell you informations on the group of Lorentz transformations...

 

[Layman FJ]

Thanks