[Pmb (OP)]

Do you all know the relationship between coordinate systems and geometric objects? What I'm curious about is how well the notion of geometric object is understood by the physics enthusiasts. What do tyou think the definition of geometric object is? I got into a discussion somewhere on this. It turns out that nobody understood it. I was shocked.

Thanks for satisfying my curiosity on this point.

[Bill S]

What do you think the definition of geometric object is?

My (very limited) understanding is that geometric objects are points, lines, curves, conic sections etc; as distinct from geometric shapes, which are squares, triangles, circles etc.

I bet you were looking for something more esoteric.

[Pmb (OP)]

What do you think the definition of geometric object is?

My (very limited) understanding is that geometric objects are points, lines, curves, conic sections etc; as distinct from geometric shapes, which are squares, triangles, circles etc.

I bet you were looking for something more esoteric.

I'll answer that later. Right now I'm trying to get a feel for what people think of when they hear that term. I was unfamiliar with what people think it means. I only know how the term is defined in differential geometry.

[Pmb (OP)]

I thought of a manifold being defined by points/events, on that manifold each observer creates their own coordinate system/frame of reference as dictated by their observations as they move about that manifold.
In other words, their experience of the manifold points/events may not be the same as other observers.
Energy/mass alter that manifold so that it, the manifold, is not the same everywhere.

I agree with everything you say here.

This maybe gobbledygook and completely off topic... so I won't go on.
Well, you did ask. No laughing there.

Not gobbledygook but not related to the subject. Thanks for posting though. I always appreciate what you have to say LB!