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berkan

A sphere has ____ sides.

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A sphere has _____ side(s).

Fill in the blank, thats all.

 

a) one

b) no

c) infinate

d) :confused:

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All of the above, depending on how you interpret it.

 

C is the usual interpretation.

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What kind of sphere are you talking about. It doesn't matter. I would say B or C depending on how you interpret it.

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Huh? There's only one 'type' of sphere, if you can even call it that.

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No, there are zero-spheres, one-spheres, and two-spheres. How could the mathematics moderator not know that?

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Probably because I'm not a great fan of topology/geometry. I'm not infallible you know, and I certainly don't claim to know everything about spheres. I try my best.

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Well, I choose D, i have no idea, and neither is it important in any way...

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I thought we established it was 0 or 1 in the other thread.

 

You know, the thread that was locked because we'd finished with it.

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I thought we established it was 0 or 1 in the other thread.

 

You know' date=' the thread that was locked because we'd finished with it.[/quote']

Then I change my answer to the established conclusion.

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I thought we established it was 0 or 1 in the other thread.

 

You know' date=' the thread that was locked because we'd finished with it.[/quote']

 

It depends how you define 'side'.

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1) How can something have NO sides? Everything we see must have sides, to reflect light, right?

2) How can something have infinite sides? The fact that it fits in your hand proves that a sphere can't have infinite sides, right?

3) How can a sphere have one side? For it to have one side it must be a part of one plane, right?

*) Since a perfect circle is impossible, hence so is a perfect sphere. This is my conclusion: A sphere has numerous (thousands if not millions of) sides that vary along with its perfection. I know this wasn't included in my multiple-choice question; therefore I would like to add this one. I'm open to any NEW ideas.

e) Numerous (not determinable)

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1) How can something have NO sides? Everything we see must have sides, to reflect light, [i']right?[/i]

Don't confuse "side" with "surface".

 

 

2) How can something have infinite sides? The fact that it fits in your hand proves that a sphere can't have infinite sides, right?

People for some reason 'decided' that the angle between any two radii of a sphere can be halved without limit, and therefore that the arc described by the distance between the radii at the surface of the sphere had an infinite number of possible locations. My argument was that such a construct would be a mesh, not a sphere.

 

 

3) How can a sphere have one side? For it to have one side it must be a part of one plane, right?

The only reason I could find for the "1 side" argument was from the dictionary definitions, which isn't great reasoning.

 

 

*) Since a perfect circle is impossible, hence so is a perfect sphere. This is my conclusion: A sphere has numerous (thousands if not millions of) sides that vary along with its perfection. I know this wasn't included in my multiple-choice question; therefore I would like to add this one. I'm open to any NEW ideas.

e) Numerous (not determinable)

A "side" is the extrusion between two vertices. Spheres don't have vertices unless you artificially and arbitrarily apply them.

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I'm curious, how do you support your claim (whatever that may be)?

1 side or 0 sides

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My argument was that such a construct would be a mesh' date=' not a sphere.

[/quote']

 

like i said in the other thread, i consider a sphere to be a limiting form of this mesh.

 

we have to define what we mean by side as well. can everyone here please write down what they think a side is.(of a 3 dimensional object of course)

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I myself want a good definition of "side", and how it defers from "surface".

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I think that the sphere has one side since the definition of a side is:

 

Mathematics

 

1. A line bounding a plane figure.

2. A surface bounding a solid figure.

Since a sphere has a one surface it has one side.

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I myself want a good definition of "side", and how it defers from "surface[/i']".

 

a surface is :

 

1.The boundary of a three-dimensional figure.

2.The two-dimensional locus of points located in three-dimensional space.

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I'm curious' date=' how do you support your claim (whatever that may be)?

[u']1 side[/u] or 0 sides

Read the other thread, then this one.

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Sometimes we think of sides as having to be flat - what mathematicians

call "faces" of a polyhedron. In that sense, a sphere has no sides

(though some people will try to convince you that it has infinitely

many sides).

 

I think the most applicable definition is the one used in topology. We

talk about surfaces with two sides (like a piece of paper) and

surfaces with only one side (like the Moebius strip you may have heard

of). In this sense, and remembering that mathematicians define a

sphere as the surface of a sphere, not a solid ball, I would say that

a sphere has two sides: the outside and the inside.

 

(ref: Dr P. APP)

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I thought sides had to be flat.

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So, to summarise:

 

We can make arguments for 0, 1 or 2 depending on the definitions we are using, but no good argument for "infinite".

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I think that this topic has been completely exhausted. It's all a matter of definition, which personally I find rather dull. But anyway, does anyone have anything fresh to add to the topic? Otherwise, I'd rather just close it.

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