Circle.

[ydoaPs]

why would it shrink?????????? if the radius shrank, wouldn't there be no circle if it got close enough to c?

[Cap'n Refsmmat]

It may become a dot, but if you zoom in close enough it's still a circle.

[Sayonara]

why would it shrink?????????? if the radius shrank, wouldn't there be no circle if it got close enough to c?

Only in the same way that there would be no circle due to the circumference shrinking, one would assume.

 

If the circumference shrinks, the radius shrinks "automatically". Of course that assumes Euclidean geometry, which after a mammoth ammount of tooth-pulling we learn is left behind in this example.

 

Considering you set this thread up to explain the phenomenon I don't see why it should be so difficult for us to extract explanations for it.

[ydoaPs]

is there a way to calculate how much the circumference shrinks relative to speed?

[Cap'n Refsmmat]

why would it shrink?????????? if the radius shrank, wouldn't there be no circle if it got close enough to c?

Can't you just give it up? You're not really contradicting us, just continually stating a new reason that you are right.

Plus you're giving yourself a bad reputation.

[jordan]

the radius only has one dimension and it doesn't shrink due to motion. the cercumference has nothing to do with if an object is a circle; it is just the length of the distance from one point in the set to itself.

 

 

edit: it still has the same equation' date=' it is still a circle.[/quote']

First, doesn't the radius have two dimensions. And second, wouldn't it experience the exact same relativistic effects as the circumfrence because it's basicly just an extension of the circumfrence. It would spin in the same direction and at the same velocity.

[Cap'n Refsmmat]

The radius is a line segment. Lines are one-dimensional.

[Sayonara]

is there a way to calculate how much the circumference shrinks relative to speed?

I would have thought so, but I don't think it will "outlast" the radius. You can't have one without the other.

[Cap'n Refsmmat]

It is sort of an extension. It's proportional to it, that's why. Proportional by .

Oh wait, you think that's wrong. Sorry.

[ydoaPs]

being proportional doesn't make it an extension

[Cap'n Refsmmat]

Does it matter?

[Aeschylus]

Do you know of any representations of that geometry I can take a look at?

 

If you have a globe in your home that is problem one of the best ways to look at it, because it has the great circles marked in it (the equator and the lines of longitude or 'meridians'). You should see that any circle drawn om the globe has a radius larger than a Eucldean circle's radius of the same circumfenrce (though the ratio tends to pi as r tends to zero) simalirly you can see that the angles of triangles always add up to more than 180 degrees (again though the sum tends to 180 as the area of the triangle temds to zero).

http://mathworld.wolfram.com/SphericalGeometry.html

[Sayonara]

If you have a globe in your home that is problem one of the best ways to look at it' date=' because it has the great circles marked in it (the equator and the lines of longitude or 'meridians'). You should see that any circle drawn om the globe has a radius larger than a Eucldean circle's radius of the same circumfenrce (though the ratio tends to pi as r tends to zero) simalirly you can see that the angles of triangles always add up to more than 180 degrees (again though the sum tends to 180 as the area of the triangle temds to zero).

http://mathworld.wolfram.com/SphericalGeometry.html[/quote']

A much better explanation.

 

My question now is: can we consider a circle to be equal to a great circle?

[ydoaPs]

perhaps the radius bends into a new dimension. the circle becomes a 2 dimensional bowl?

[Aeschylus]

A much better explanation.

 

My question now is: can we consider a circle to be equal to a great circle?

 

We can consider a great circle to be a special case of circles in spherical geometry.

[ydoaPs]

how did it go from being flat, to being a circle drawn on a sphere?

[Aeschylus]

how did it go from being flat, to being a circle drawn on a sphere?

 

how did what go from flat......?

[Sayonara]

how did it go from being flat, to being a circle drawn on a sphere?

How can you not be following this?

 

I am starting to think you know the conclusion but not the explanation.

[Sayonara]

We can consider a great circle to be a special case of circles in spherical geometry.

I'm guessing that taking the shortest radius of the circle described by the circumference of the great circle is cheating?

[ydoaPs]

i don't know the "answer." it went from being a flat circle to being on a globe. how did that happen?

[Aeschylus]

I'm guessing that taking the shortest radius of the circle described by the circumference of the great circle is cheating?

 

Well on sphere of radius R (though rember that R can just be parameter describing the geomery it needn't be the radius of any actual sphere) the circumeference of the great cricle is:

 

2pi*R, but the radius is pi*R/2

[Aeschylus]

i don't know the "answer." it went from being a flat circle to being on a globe. how did that happen?

 

If your talking about the relativstic disc, I posted a link a few pages back which explains the scenatio in detail.

 

I'm just using spherical geometry as an example of non-Eucldean geometry.

[osram]

The radius isn't an object affected by relativity.

The radius is a line only in your imagination.

The circle however is an object affected by relativity and will shrink when it's rotating (around a line perpendicular to the circle plane).

When circumference is shrinking the radius will too...

 

Which means it's still a circle, just a bit smaller.

[ydoaPs]

i still don't see why everyone is assuming the radius would shrink

[Sayonara]

i still don't see why everyone is assuming the radius would shrink

Because the (euclidean) radius is the distance between the circumference and the centre of the circle.

 

We have provided a reason; you have not.