I Mobius Transformation: Physical Significance?

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Mobius transformations in geometry assume that a line can be viewed as a circle of infinite radius, raising questions about their physical significance. These transformations map straight lines to lines or circles and circles to lines or circles, utilizing stereographic projection from a plane to a sphere. In physics, they are associated with the group structure known as SL(2, C), which provides insights into Lorentz transformations. This connection highlights the relevance of Mobius transformations in understanding geometric and physical phenomena. The discussion emphasizes the interplay between geometry and physics through these transformations.
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In Mobius geometry it is assumed that a line is a circle of infinite radius.Does this have any physical significance?
 
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