Concentric circles are parallel?

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Concentric circles can be considered parallel under certain definitions, particularly when the concept of parallelism is generalized beyond straight lines. The discussion highlights the distinction between Euclidean geometry, which defines parallelism strictly for lines, and other interpretations that may include curves. Participants debate the nature of parallelism, questioning whether curves can be parallel and how definitions may vary across different geometrical contexts. The conversation emphasizes the importance of clearly defining "parallel" to avoid confusion, particularly when discussing non-Euclidean geometries. Ultimately, the definition of parallel can extend to curves if one adopts a broader perspective, but this is not universally accepted.
  • #211
To add concentric circles to our definition of "parallel lines," you would have to prove all the rules for parallel lines apply. One of those rules has to do with parallel lines intersecting other parallel lines (corresponding angles are equal). Can you show me even one that works? (ALL should work if what you say should be accepted.)
 

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  • #212
AC130Nav said:
To add concentric circles to our definition of "parallel lines," you would have to prove all the rules for parallel lines apply. One of those rules has to do with parallel lines intersecting other parallel lines (corresponding angles are equal). Can you show me even one that works? (ALL should work if what you say should be accepted.)

The straight line parallel has the phase angle to be equal, generally, the curve parallel does not have the corresponding angle to be equal.
 

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