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## Main Question or Discussion Point

God knows if I'm posting this in the right place on physics forum but here goes...

If a circle can be thought of as a shape with an infinite number of sides does this then therefore mean that each side would have to be infinitely small?

Within a large circle you can draw a smaller circle inside it. If both the small and large circle has the same number of sides – an infinite number – then does this mean that the large circle has side lengths that are longer than the small circle?

Also, if a value is assigned to the sides of circle then would this then mean that the circle would be infinitely large?

I hope that someone can make sense of my questions and point out where in my thinking that I’m going wrong.

I’ve done some research and found one person claimed that:

Another person thought that:

They thought this because The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. Therefore this is the smallest measurement of length with any meaning.

Yet another claim was that:

The 4th claim was:

I don’t know enough mathematics to be able to assess any of these four claims.

So which is it? Do circles have?

a. Infinite number of sides

b. A very large but finite number of sides

c. Zero sides

d. 2 sides

I’ve also read that it all depends on what your definition of a side is.

If a circle can be thought of as a shape with an infinite number of sides does this then therefore mean that each side would have to be infinitely small?

Within a large circle you can draw a smaller circle inside it. If both the small and large circle has the same number of sides – an infinite number – then does this mean that the large circle has side lengths that are longer than the small circle?

Also, if a value is assigned to the sides of circle then would this then mean that the circle would be infinitely large?

I hope that someone can make sense of my questions and point out where in my thinking that I’m going wrong.

I’ve done some research and found one person claimed that:

*When one does calculus, it is assumed by the notion of taking limits for tangents of any curve that a circle can be thought of as a polygon with an infinite number of sides, each of infinitesimal length.*Another person thought that:

*The number of "real" sides of a particular circle would be its circumference in units of the Planck length. This would be a big number, but not infinite.*They thought this because The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. Therefore this is the smallest measurement of length with any meaning.

Yet another claim was that:

*To have a 'side' you need to have 3 collinear points. But a circle doesn’t have 3 collinear points. Thus it has 0 sides.*The 4th claim was:

*A circle has 2 sides because the standard form the circular equation is (x-x1)^2+(y-y1)^2=r^2*I don’t know enough mathematics to be able to assess any of these four claims.

So which is it? Do circles have?

a. Infinite number of sides

b. A very large but finite number of sides

c. Zero sides

d. 2 sides

I’ve also read that it all depends on what your definition of a side is.