If we have a 2 dimensional plane and roll it into a cylinder, is it now a 3 dimensional object or is it a 2 dimensional object.
Care to discuss?
Care to discuss?
The flat sheet is the 2D surface formed by sweeping out a 1D straight line. The tube is a 2D surface formed by sweeping out a 1D closed line i.e. circle. So in purest mathematical sense it remains 2D. In physical reality it is a 3D body with large aspect ratio(s), since to exist as a self-supporting object it must have finite sheet thickness, hence finite 3D volume.If we have a 2 dimensional plane and roll it into a cylinder, is it now a 3 dimensional object or is it a 2 dimensional object.
Care to discuss?
ok so in Math it is 2 dimensional but in Physics it is 3 dimensional... ok I can go with that... nice....thanks!The flat sheet is the 2D surface formed by sweeping out a 1D straight line. The tube is a 2D surface formed by sweeping out a 1D closed line i.e. circle. So in purest mathematical sense it remains 2D. In physical reality it is a 3D body with large aspect ratio(s), since to exist as a self-supporting object it must have finite sheet thickness, hence finite 3D volume.
Tell me . . . . is it rolled into a third dimension? therein lies your answer . . . . .If we have a 2 dimensional plane and roll it into a cylinder, is it now a 3 dimensional object or is it a 2 dimensional object.
Care to discuss?
You present some valid points, Dinosaur!It is a 2D surface.
A solid cylinder would be a 3D object, although plane geometry would be applicable to the surface.
Plane geometry is applicable to this surface, although plane topology might not be.
Note that the Pythagorean formula can be used for right triangles.
If you apply differential geometry to this surface, the metric is the same as that for a plane.
Similar remarks apply to any surface which can be cut & flattened without crinkling.
There is a more formal way to express the above remark. I do not think that crinkling term in the above context.
It is a 2D surface.
Shouldn't that readYou can't roll a 2 dimensional object.
Edit: I forgot to dress my statement up for crankdom..."You can't roll a 2 dimensional object according to mainstream scientific theory".
valid point!Tell me . . . . is it rolled into a third dimension? therein lies your answer . . . . .
Wrong. A sphere i.e. spherical surface remains 2D. A ball is the solid filled 3D analogue of a 2D sphere. To be fair, there is common use of sphere to mean ball even among academics who know better.Since we are not (yet) too deep into this discussion, I would propose (IMO) that the above ROTATIONAL operation represents a physical and mathematical transformation from 2-D to 3-D. Rotation is an operator that introduces a dimensional transformation. Similar to starting with a circle and rotating the circle. As long as the circle is rotated about its circumfrence, within its original 'planc', it remains a 2-D circle. When 'translated at a right angle to that original plance, it describes a tube (similar to original argument). When rotated 360 deg. from the original plane, about a line bisecting the circle, the pi function is again introduced which generates a 3-D sphere. Not too disimilar to crystalographic symmetry operations involving translational, rotational, inversion, and mirror (and combinations thereof) operators. Just my non-mathematician's opinion!
For the second time - or has your #3 been forgotten already? No need to reply btw. It would be nice if this thread quietly died sooner rather than later. Against SF tradition I know.Actually even though I am totally naive this sounds very convincing.
In physics or mathematics how would one define the word "discussion" as in "discussion forum" as in sciforum's being a place to discuss things....For the second time - or has your #3 been forgotten already? No need to reply btw. It would be nice if this thread quietly died sooner rather than later. Against SF tradition I know.
Notwithstanding the snobbery and overly restrictive conservative policies often arbitrarily applied at PhysicsForums.com, I suggest you contrast the general mayhem and waffle here with the situation over there. Any subforum except for the 'free thoughts' variety.In physics or mathematics how would one define the word "discussion" as in "discussion forum" as in sciforum's being a place to discuss things....
Of course - additional info needs to be specified. Let's see, still only page 1. OK so far.is there any way you can determine whether this (example below) is an image of an opaque sphere (2d surface) or a ball...no need to answer as it appears obvious.. "no"
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fully appreciate your concerns Q-reeus! But this is not PhysicsForums this is sciforums and we have all sorts of interested members posting all sorts of stuff most of which is more akin to chit chat rather than genuine scientific pursuit.Notwithstanding the snobbery and overly restrictive conservative policies often arbitrarily applied at PhysicsForums.com, I suggest you contrast the general mayhem and waffle here with the situation over there. Any subforum except for the 'free thoughts' variety.
is there something of interest in this subject you wished to discuss ? Something that would extend the conversation in a way that ultimately benefits you?Notwithstanding the snobbery and overly restrictive conservative policies often arbitrarily applied at PhysicsForums.com, I suggest you contrast the general mayhem and waffle here with the situation over there. Any subforum except for the 'free thoughts' variety.