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A sphere has ____ sides.


berkan
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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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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[/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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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 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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