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

[IWantGod]

Is that a Hyper-cube?

(Please Note: This uploaded content is no longer available.)

 

[Cruciferi]

A Tesseract is a four-dimensional hypercube.

 

[1Lord1Faith]

Looks two dimensional to me. Or is it four dimensional in spirit?

 

[dochawk]

I think its fine here…it has a philosophical element to it.

Only in the sense that “Can 3 be equal to 4” has a philosophical element.

Given the definitions of circles and radii, the question answers itself.

It’s not “philosophical”, but “sophomoric”. They’re not the same . . .

hawk

 

[Hereiam]

The bigger question is, do you find it offendive to be posted here? If you dont its a nonsequitor…if you do, you should click on the flag.

 

[thistle]

It seems like you have been googling for a question to put to us!!

 

[george.s.v]

Cruciferi:

A circle always has a radius, circumference, and diameter.

Yes but can it remain a circle as defined by its radius, circumference, and diameter, while also being infinitely small?

An infinitely small circle does exist, and it has, obviously, infinitely small radius, circumference, and diameter…

 

[TechieGuy]

Please define “infinitely small” and “radius” and which geometric model you are using - euclidean, hyperbolic, or some other.

 

[Theo520]

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

I don’t find the question clear. what do you mean by ‘retain it’s radius’?

By definition, every circle has a radius and diameter, and every different size of circle has a different measurement of radius and diameter.

If a circle lost it’s radius, then perhaps you should call it a point.

 

[BartholomewB]

Yes but can it remain a circle as defined by its radius, circumference, and diameter, while also being infinitely small?

An infinitely small circle has a radius of 1/∞ (one over infinity). It also has a diameter of 1/∞. It also has a circumference of 1/∞. Does this mean there is such a thing as a circle whose radius is equal to its diameter and also to its circumference? I suspect the answer is No, but I’d have to ask a professional mathematician.

 

[Theo520]

An infinitely small circle has a radius of 1/∞ (one over infinity). It also has a diameter of 1/∞. It also has a circumference of 1/∞. Does this mean there is such a thing as a circle whose radius is equal to its diameter and also to its circumference? I suspect the answer is No, but I’d have to ask a professional mathematician.

There is always room for more decimal places, so a circle’s radius never equals the diameter unless you are rounding.

 

[Brendan_64]

So you don’t think it would be squished in to an infinitesimal point and therefore lose what defines it as a circle?

Then it would not be a circle so the question of whether it has a radius would not apply.

 

[XndrK]

1/infinity isn’t a useful term, so you would have a circle with a radius, diameter, and circumference of 0 if you tried. It would still be a circle – you defined a circle with radius zero and all the weirdness that implies – but mathematically there are very few reasons one would do such a thing.

 

[DaveBj]

How many angels can dance inside this circle?

Beat me to it And cool animated tesseract! When my high school classes got boring, I would try to draw a tesseract. Never got that down. Must have been the two-dimensional paper

Back on topic, and bringing up my memories of high-school geometry, if a circle is infinitely small, it fits the definition of a point, and therefore it is no longer a circle, and therefore it has no radius.

D