A Question Of Dimensionality

[Quantum Quack]

If you take a 2 dimensional rectangular plane and curl it into a cylinder is the cylinder considered as 2 dimensional or 3 dimensional?

[scameter]

well, i'm really not sure. before we proceed, could someone define a plane to me, please? i haven't taken geometry yet, i am sorry.

[Quantum Quack]

a 2 dimennsional plane is a surface that has only width and height. Having no depth it is similar to what you are seeing on you pc monitor.

If you take this plane and curl it into a cylinder is the cylinder 2 or 3 dimensional?

eventually this leads to the notion of a 3 dimensional circle or a coil if the depth of the circle dimension is described as time.

[todd]

In a three-dimensional x-y-z coordinate system, a plane is the set of all solutions of the following equation

ax + by + cz + d = 0,
a,b,c,d real numbers non0 simultaneously

or: a surface containing all the straight lines that connect any two points on it

[scameter]

well, that denpends then i guess on if one can count it's inner area or not. if not, then it is still merely two dimensional, just curved. but, if you count the inner area too, then it could be 3 dimensional because it would have depth. and, something else is is how can anything possibly have absolutely no depth? i mean, even if it is so thin that we can not see it by any means, how could it still have no depth? or is this just math, not physical logic?

[todd]

Any plane surface can be considered to be a sphere with infinite radius.

3 dimensions don't necessarily mean depth. Depth means volume. A 3d surface doesn't have volume.

[Thomas Knierim]

If you can follow a path from the cylinder's wall to the opposite wall straight through the middle without following the circumference, it's 3-dimensional, otherwise it is 2-dimensional and the 3rd dimension is only conceptual.

Cheers, Thomas

P.S.: Sorry, forget that. You can easily create a 2-dimensional topography like that.

[scameter]

but, it would still have some volume thought wouldn't it? does everything not have some volume? even an electric current or light has some volume, even if it is impossible for us to see?

oh, and another question i have is is how is electricity related to light?

[todd]

A mathematical surface is usually a 3d surface, or a plane with only 2 dimensions.
I think your question is mostly about the surface and not to plane or dimensions
So this is not about 2d and 3d.
Your question is if in fact a surface has depth(volume).
The mathematical surface has no volume, is purely imaginative, conceptual.
In reality there is no such thing as volumeless surface. Any physical surface has a depth and therefore a volume
This is the same with considering the volume of a point in 3d or its area in 2d

[scameter]

ok, yo answered my question exactly. thank you. :)

[sonrisa]

Originally posted by scameter
oh and another question i have is how is electricity related to light?

well when you flip on a light switch the electricity turns on the lights! :D

seriously, Benjamin Franklin demonstrated that back in 1752, when he showed that lightning is a form of electricity. If I remember my science correctly, when electrons become charged into ions they give off blue-white sparks. When enough of these ions glom together they form lightning. If you can channel the lighning on a wire (form a current) then you can make electric lighting. If anybody can improve on that explanation please feel free to do so since it's been awhile since I studied electricity.

[scameter]

well, that wasn't exactly what i meant by light(not lighting :D) and there is alot more to it about both lightning and electrical engineering and such, but my real question was, in a more essential manner, is thus: How is electricity related to photonic, common, uncontained light?

[sahyo]

How is electricity related to photonic, common, uncontained light?

minus 'related"


................................;)

[scameter]

and then pluss again lol or do you mean it is not at all? :lol:

[sahyo]

hehehe

electriclight

:D

[scameter]

:lol: luminous electricity :D

[sahyo]

:D

[scameter]

ok, seriously: how are electricity and light related?

[todd]

theoretically, a change in the electron's energy level results in the emission of a photon, so therefore, light.

[scameter]

which is essentially how a light bulb works?

[sahyo]

ok, seriously: how are electricity and light related?



th :blink: inking "re :blink: alated" as though se :blink: parate?

[scameter]

not all things related have to be seperate. for instance, the skin on my knee is related to the skin in my mouth, and are together, connected, not seperate. but, i do like your use of contractions :D

[sahyo]

not all things related have to be seperate.

ohoh oingoboingo

for instance, the skin on my knee is related to the skin in my mouth, and are together, connected, not seperate.

body without body

but, i do like your use of contractions :D

hehe

:D

[scameter]

:rolleyes: :D

[sahyo]

:lol: :D

[scameter]

:D

[scameter]

Bito: The mathematical surface has no volume, is purely imaginative, conceptual.

....which is why i hate math. it is not real, it is conceptual. i like science, and even logic, but not math. math is lifeless, destitute, fake. and, unfortunately, it has managed to taint many of the other studies with it's deathliness, for example, the increasing importance of grammer on words. mathematical logic is trying to make everything like it, dead, and grammer makes words seem dead, lifeless, very unfortunately. i think logic and grammer are important, but they should not make a screen for words over the most important thing about them; their meaning and beauty, two things for which seem nearly forgotten by the majority of people.

[zewc]

How is light related to electricity? By four very simple equations (well, simple if you are up on your calculus!) and these are the Maxwell Equations. Wonderful equations.

As stated before, the transition of electrons in atoms, from a higher energy level to a lower does result in the emission of photons (i.e. light). But as for a light bulb, the current that passes through the filament in the bulb heating it up, then, the thermal energy in the filament builds up until it it hot enough to emit light. These emitted photons are from the excited atoms in the filament.

Need futher explaination? :think:

Electricity can be thought of as the movement of electrons around a circuit.

Light is more difficult, but is related to electricity as per the Maxwell equations. To explain any more would require some equations, which i will post at request! :thumbsup: