## Circle becomes a pair of parallel lines

Does anyone know if there is a non-Euclidean geometry(or something like that) where the circle becomes a line or a pair of parallel lines?

...or even where the circle becomes a set of parallel lines?

...i'm doing some work in Guitar Theory and this situation appears...

Thanks

The Roman Empire Guitar Research Institute

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 Recognitions: Gold Member Science Advisor Staff Emeritus It's hard to believe you are serious, but no, all different "geometries" respect the fundamental topological properties of sets. In particular, if a set is connected (as is a circle) in one geometry, it will be connected in any geometry (and "parallel lines" are not connected).
 I'm serious! But are you sure about your answer? I study a little Math also...I'm more on the Algebra 'side'...(i finally reached Group Theory proper...thank God!) BUT isn't there something about something becoming great circles....or something about great circles becoming something...etc...etc...? Isn't there a situation where a line becomes a great circle? Thanks

## Circle becomes a pair of parallel lines

 Quote by zmodnz I'm serious! But are you sure about your answer? I study a little Math also...I'm more on the Algebra 'side'...(i finally reached Group Theory proper...thank God!) BUT isn't there something about something becoming great circles....or something about great circles becoming something...etc...etc...? Isn't there a situation where a line becomes a great circle? Thanks
If sounds like you're thinking of the geometry on a sphere--I've heard that geometry be referred to as "Riemannian" geometry, but I've also heard "Riemannian" refer to a much more general class of geometries. In the geometry on a sphere, the geodesics ("straight" lines) are great circles of the sphere. Doesn't that intuitively seem like the shortest way to get from one point to another?

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