Can a Circle be infinetly small and at the same time retain its radius?

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Can a Circle be infinitely small and at the same time retain its radius?.
 
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A circle always has a radius, circumference, and diameter. Not sure what the point of this is 😐
 
Its just a qeustion. Can you answer it?
 
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Cruciferi said:
A circle always has a radius, circumference, and diameter.
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Yes but can it remain a circle as defined by its radius, circumference, and diameter, while also being infinitely small?
 
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This isn’t a Catholic topic…should probably be closed.
 
IWantGod said:
Yes but can it remain a circle as defined by its radius, circumference, and diameter, while also being infinitely small?
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I think it would because radius, circumference, and diameter are all proportional to the size of the circle.
 
Hereiam said:
I think it would because radius, circumference, and diameter are all proportional to the size of the circle.
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So you don’t think it would be squished in to an infinitesimal point and therefore lose what defines it as a circle?

I have been thinking, what if size is purely relative? What if in principle there is no limit to how small or large a thing is. You never get to a point where a thing is too small to be a circle, and therefore a thing can retain its shape or dimensions… Could this be applied to reality?
 
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I do think if it were infinitesimally small, it would be a point. A circle requires two dimensions, not zero or one.
 
IWantGod said:
So you don’t think it would be squished in to an infinitesimal point and therefore lose what defines it as a circle?

I have been thinking, what if size is purely relative? What if in principle there is no limit to how small or large a thing is. You never get to a point where a thing is too small or too big, and therefore a thing can retain its shape… Could this be applied to reality?
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I think proportion is relative, not size. So there is no limit to how small or large a thing is. Shape would be continual, because as “size” of circle increases or decreases the diameter, circumference and radius would increase or decrease proportionately.

Image a diagram of a circle on your computer screen showing diameter, circumference and radius…then shrink the view. The circle is smaller but so are the diameter, circumference and radius in direct proportion to the reduction in size of the circle on your screen…and so it would go, no matter how much you magnified or shrunk the image…sure at some point, the naked eye may not be able to perceive the circle, but its constitution by mathematical law would remain.

Does it apply to reality? Well there is the philosophical question! It applies to the reality of the circle, but, wow, on the application to reality…this would be a topic to have over a nice pot of tea!
 
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How many angels can dance inside this circle? ⭕
 
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Indeed, it can have other attributes as well. Whatever you want.
 
Usagi, What do you think of what Hereiam said?
Hereiam said:
I think proportion is relative, not size. So there is no limit to how small or large a thing is. Shape would be continual, because as “size” of circle increases or decreases the diameter, circumference and radius would increase or decrease proportionately.

Image a diagram of a circle on your computer screen showing diameter, circumference and radius…then shrink the view. The circle is smaller but so are the diameter, circumference and radius in direct proportion to the reduction in size of the circle on your screen…and so it would go, no matter how much you magnified or shrunk the image…sure at some point, the naked eye may not be able to perceive the circle, but its constitution by mathematical law would remain.

Does it apply to reality? Well there is the philosophical question! It applies to the reality of the circle, but, wow, on the application to reality…this would be a topic to have over a nice pot of tea!
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IWantGod said:
Can a Circle be infinitely small and at the same time retain its radius?.
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There is a set containing a converging sequence and there is the limit to that sequence. The sequence consisting of circles in the plane with center at (0,0) and radius 1/n will converge to the limit point (0,0) as n increases. Each circle in the sequence is a circle of non-zero radius 1/n. The limit point (0,0) is not usually thought of as a circle, although I suppose it is possible to think of it as a circle of radius 0. Calculus 101.
 
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Well can a single point be ever drawn? Or is it always a blob of circle?
 
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I found camels 🐪 inside the circle contained within a needle.
 
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