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?
2 dimensions into 3 dimensions
- Thread starter Quantum Quack
- Start date
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.
Are we done here, or is there an urge to beat the 20-page rambling chit-chat BS over in that other thread you started recently?
ok so in Math it is 2 dimensional but in Physics it is 3 dimensional... ok I can go with that... nice....thanks!
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!
Last edited:
Tell me . . . . is it rolled into a third dimension? therein lies your answer . . . . .
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.
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.
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.
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.
You present some valid points, Dinosaur!
Actually even though I am totally naive this sounds very convincing.
Shouldn't that read
"You can't roll a 2 dimensional surface according to mainstream scientific theory"
valid point!
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.
To create a ball one sweeps a semi-circular area about an axis running along the straight edge boundary. Pretty obvious. In general, sweeping an area along an axis not lying in the plane of such an area generates a 3D object. Again - intuitively obvious.
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.
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....
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"
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.
Of course - additional info needs to be specified. Let's see, still only page 1. OK so far.
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.
You have posted a very articulate response and I and many others are grateful for your ongoing participation as it tends to keep the waffle down a little...
Q-reeus: You are probably techically/mathematically correct. The point I was making (mainly) is that when you rotate a surface INTO an additional dimension that is NOT the original 2-D depiction, you increase the dimensional attributes. 2-D surfaces thus rotated assume attributes of 3-D structures. Since I am not a technical mathematician, I won't argue this point further, except to reiterate (IMO) that 2-D surfaces rotated (or transformed) as described assumes 3-D attributes. Projection accomplishes the opposite effect - for example, one can reduce the dimensional attributes by 'projecting' (from a preferred POV) a 3-D entity to a lower dimensional (2-D) aspect - not unlike 'shadows cast on a cave wall'.
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?