Radius question

Mar 2015
213
5
England
Is a radius, in a 3D sphere, considered to be a 2D object?
I would argue it is, because, it's drawn from the centre (internal middle) to a point on the external surface area, thus having length and height.
 

SDK

Sep 2016
789
537
USA
Is a radius, in a 3D sphere, considered to be a 2D object?
I would argue it is, because, it's drawn from the centre (internal middle) to a point on the external surface area, thus having length and height.
A radius is just a number. If you are asking about a radial line segment then this is a 1-dimensional object no matter the dimension of the sphere.
 
Mar 2015
213
5
England
That's interesting, I just googled radial line segment and it says.
'A radial segment is the area enclosed between two radii, and the portion of the circumference, and a segment of the circle is a part of the circumference.'
Area suggests it's a 2D shape, let's hear what other people have to say.
Perhaps there's a difference between radial segment and radial line segment?
 

SDK

Sep 2016
789
537
USA
That's interesting, I just googled radial line segment and it says.
'A radial segment is the area enclosed between two radii, and the portion of the circumference, and a segment of the circle is a part of the circumference.'
Area suggests it's a 2D shape, let's hear what other people have to say.
Perhaps there's a difference between radial segment and radial line segment?
I don't know what you found via google, but it appears you are talking about a circular sector. To be fair, I wasn't explicit in my comment about what I meant by a radial line segment. This is why definitions in math are so important, so let's clear that up. I'm referring to any line segment between the center of a sphere and its boundary. This is always 1-dimensional, because line segments are 1-dimensional. A circular sector is usually defined as the region in the plane bounded between two radial line segments for a 1-dimensional sphere (i.e. a circle) and the boundary of the sphere. This is a 2-dimensional object.

I'm unsure what you mean by a 3-D sphere since you seem to be referring to a sphere in 3-dimensional space. But this is actually a 2-dimensional sphere due to the fact that it is already only a 2-dimensional object. Alternatively, a 3-dimensional sphere is the boundary of a 4-dimensional ball. But in either case, a radial line segment is just a line segment between the center of the sphere and any point on the boundary, so it is always 1-dimensional. In these other cases, there are ways you could generalize the notion of a circular sector, but they would require more than 2 radial line segments.

In any case, the upshot here is you should be more specific about what kind of object you are asking about. It would help if you described things clearly using sets.
 
Mar 2015
213
5
England
The 'and' implies having both properties simultaneously.

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Last edited:

skipjack

Forum Staff
Dec 2006
21,468
2,463
Do they differ in any way?