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Extraordinary claims require extraordinary proof

Where would you add the word?
Before "detect"
"Since we can't actually detect or see sub-atomic particles or events" should be "Since we can't actually directly detect or see sub-atomic particles or events", etc.
We can actually indirectly detect or see sub-atomic particles or events.
 
Today, 05:13 PM

MattusMaximus
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Today, 05:18 PM

MattusMaximus
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Today, 05:29 PM

MattusMaximus
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Today, 05:32 PM

MattusMaximus
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4 posts in 19 minutes. I think I'll keep on ignoring the troll.

I think you should put on ignore yourself.You prove that you troll yourself...
Since calling people,who knows more then you trolls is biggest mark of troll...

I do not think you want to learn anything,you are not sceptic.(When are trolls sceptics anyway? ;) )

Well,who wants to remain dumb/UNinformed,will be so.You have been categorised as woo(physic)/troll.
 
You are right - a 2D balloon has only a surface. If that seems incredible to you then what about the mobius strip - it is a surface with inly 1 side!
Depends what you mean by “surface” and “side”. Is a solid donut torus a surface with only one side?
 
Today, 05:13 PM

MattusMaximus
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Today, 05:18 PM

MattusMaximus
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MattusMaximus
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Today, 05:32 PM

MattusMaximus
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4 posts in 19 minutes. I think I'll keep on ignoring the troll.
Out of curiosity do you know what ignore means? Because I don't think the word means what you think it means.
 
No it is a solid donut torus.
Don’t understand your answer. By “solid” I only meant it’s not hollow and doesn’t have an inside surface. Let me restate the question - Does the outer surface of a donut torus (as shown below) only have one side?

250px-Torus.png
 
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Dark Matter is the same as Neutrino's? Has anyone ever suspected this before?

What's dark-energy then?
 
that 20% iswhat some call god the underlying inteligence beyond the universe
Close, but no cigar. That 20% is also Santa, the Tooth Fairy, leprechauns, elves, imaginary friends, etc. the underlying fantasies beyond the credible.
 
I'd like to thank sol invictus, Reality Check and MattusMaximus for a very informative thread. I think there were some other people in the thread, but I forget. ;)
 
Does the outer surface of a donut torus (as shown below) only have one side

No: it has two sides.

Technically, the reason is that the 2-torus (which is what mathematicians call the surface of a donut) is orientable, but the Mobius strip is not.

I'd like to thank sol invictus, Reality Check and MattusMaximus for a very informative thread. I think there were some other people in the thread, but I forget. ;)

Thanks!
 
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No: it has two sides.

Technically, the reason is that the 2-torus (which is what mathematicians call the surface of a donut) is orientable, but the Mobius strip is not.
Don’t understand why the mobius strip isn’t orientable. The edge of the strip has size and the object is 3D. What say we increase the size of the edge to the size of the side as show below? (quickly and roughly made from some old foam). In other words we make a mobius from a square section instead of a strip. Is this orientable? Does each of the two mobius strips created still only have one side?


001.JPG


An interesting thing is that if you only twist the square section by a quarter turn then four sides become one! (as below). Same with 5, 6 ,7, etc. if you just twist each by one side.

002.JPG
 
Don’t understand why the mobius strip isn’t orientable. The edge of the strip has size and the object is 3D.

The Mobius strip is by definition a two-dimensional surface. It's like the surface of the donut in that sense - it has no depth, only width and length. It's not orientable because you can't define an inside or an outside - it only has one surface.

A little more technically, imagine making a little forest of cactus spines or arrows which point up away from the surface on each side of it. If we were talking about the donut surface, there would be no problem - the arrows on the outside point out, and the arrows on the inside point in (into the donut). Now try to do that for a Mobius strip, or this Klein bottle:

http://www.ima.umn.edu/2005-2006/gallery/polthier/kleinBottleNormalShowStill_med.jpg

See the difference?
 
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The Mobius strip is by definition a two-dimensional surface. It's like the surface of the donut in that sense - it has no depth, only width and length. It's not orientable because you can't define an inside or an outside - it only has one surface.

A little more technically, imagine making a little forest of cactus spines or arrows which point up away from the surface on each side of it. If we were talking about the donut surface, there would be no problem - the arrows on the outside point out, and the arrows on the inside point in (into the donut). Now try to do that for a Mobius strip, or this Klein bottle:

http://www.ima.umn.edu/2005-2006/gallery/polthier/kleinBottleNormalShowStill_med.jpg

See the difference?
The mobius band (why call it a strip?) may be defined as a two-dimensional surface in the abstract world of mathematics, but in the actual world it’s a 3D object. Why does mathematics ignore the fact that it has an edge and a thickness (depth)?

To me your “spines” prove, not disprove, the 3D structure of a mobius band. Imagine the spines are longer in the center and progressively shorter to each side as below. The ends of the spines would effectively form a torus shape.

spines.bmp

Just in case it's not obvious - mobius is red, spines are black.

The edge of a mobius band is essentially a spiralled line around a torus . . .

torusmobius.gif
 
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The mobius band (why call it a strip?) may be defined as a two-dimensional surface in the abstract world of mathematics, but in the actual world it’s a 3D object. Why does mathematics ignore the fact that it has an edge and a thickness (depth)?

To me your “spines” prove, not disprove, the 3D structure of a mobius band. Imagine the spines are longer in the center and progressively shorter to each side as below. The ends of the spines would effectively form a torus shape.

http://www.accommodationz.co.nz/jref/spines.bmp
Just in case it's not obvious - mobius is red, spines are black.

The edge of a mobius band is essentially a spiralled line around a torus . . .

http://www.accommodationz.co.nz/jref/torusmobius.gif

The spines are not real. They are an aid in thinking about the orientability of the surface.
 

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