Please give the definition of parallel lines(generalised circles) in inversive geometry? Is there a unique definition (because i am confused about the duality of line with circle)? If parallel is defined only for straight lines then how can we define parallel for generalised circles?
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Circles through that intersect the center of the circle of inversion map to lines.
Lines then map back to circles.
With the exception of lines through the center of the circle of inversion, which don't go anywhere.
Parallel lines will map to circles that kiss at the center of the circle of inversion.
If the light circle is the circle of inversion, the parallel lines map to the kissing circles, and the kissing circles map to the parallel lines.
Doug M
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Please suggest some reference. – user402705 Dec 30 '16 at 01:18
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Is it correct to say that parallel lines will be concentric circles ? – user402705 Dec 30 '16 at 01:59
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Not concentric, kissing. – Doug M Dec 30 '16 at 17:11