How many sides does a circle has.

After reading all the response before mine, my brain hurts.

I would say an infinite amount of sides because as we increase the number of side in the polygon, the image appears more circular...approaching infinity.

Then again I might state zero...because it seems by definition of all other polygons, the side is defined as a straight line along he border of the figure. A circle has no such straight lines (unless we consider the infinite theory above) so by definition, there are no sides.

Then again, I might say one because a side may be defined as an single drawn line which has no defined angle...thus it;s not the sides that define a polygon but the number of angles. So in this case, there might be one side....unless one considers the infinite scenario above.

Juggling the three, I would submit that the answer is theoretically "Infinite"...with strong arguments of the other two answers.

My brain still hurts.

Two. The inside and the outside.

None. A 'side' necessarily implies one of multiple sides. This is impossible with either the inside or outside of a circle. A circle is but a perfect closed-loop line.

2. the inside and the outside

That's a question for a psychologist ;)

For those who are thinking that the answer is lim𝑛→∞𝑛=∞
lim
n
→
∞
n
=
∞
, via:

An 𝑛
n
-gon has 𝑛
n
sides;
A circle is a limit of a 𝑛
n
-gon as 𝑛→∞
n
→
∞
;
Therefore a circle has lim𝑛→∞𝑛=∞
lim
n
→
∞
n
=
∞
sides;
I'd like to mention: it's not so straightforward. If taking limits in this way were legitimate then we can show that e.g. a square has an infinite number of sides.

Consider a staircase with 𝑛
n
steps, and each step has height 1/𝑛
1
/
n
and width 1/𝑛
1
/
n
. It consists of 2𝑛
2
n
line segments. As 𝑛→∞
n
→
∞
, the staircase converges to a single line segment (i.e. the limit agrees point-for-point with a single line segment).

If we glue four of these staircases together, and take their limit, we obtain a square, which would have lim𝑛→∞4×2𝑛=∞
lim
n
→
∞
4
×
2
n
=
∞
sides.

I thought more on this question this morning and the variance in answers stems from the ambiguity in what is being considered a side. The answer changes if we are answering the question of sides as a function, a concept, or as a riddle (more philosophical.) Without a more precise definition of a side and methodology used to define the circle there is truly no way to answer this question definitively.

a circle has no sides, it's the reason so many churches are round now days

This question was asked on Ouara once. The answer is so long and drawn out in it's explanation that I had no chance of following it being as I failed basic math.
The true answer as it was answered on Quara by someone who appeared to really know what they were talking about because they were giving equations and crazy stuff like that is one.
I thought two just like a lot of people do because to me a circle with only one side would actually be a sphere.
But also a circle with two sides wouldn't be a circle it would be a ring.
So I would have to go with one because it isn't a sphere nor a ring.
One I say. LOL
I wrote way to much.

two

Sides is usually synonymous with edges so one

[image deleted]Give me a minute! 🤔

I have to say to the group that it was refreshing to see an expansive dialogue NOT containing screaming political name calling or genitalia displays. There may actually be a hint of civility on this site after all.

We discussed it in the group and it said infinity again. When we integrate its approaching infinity and external angle is approaching zero not that it is exactly zero.

So, for the sake of convinience, we take the number of sides as infinity as it is -> infinity.
External Angle is - > zero but we take it as non zero or may be 0.0000000000000001 of a Degree.

It has 2 sides.

Inside and outside.

One..

Infinite number of sides because it's a circle

One side

Ok, I will offer three distinct answers to your question.

Answer No. 1.
A circle is by definition a two dimensional construct. It exists on a single plane. It is one line with its ends connected to each other.

Any line on a plane has two sides, as there are two dimensions to a plane. Those two sides to the line can be described as left and right, top and bottom, or upper and lower. All of those names describe the same set of two sides. There are but two sides to any line in any plane.

"Inside and outside" is a set of names accurately representing the very same two sides such a line has on that very same two dimensional plane.

Regardless of the position of the single line defining the circle it still has two sides and two sides only. One for each dimension of the plane. The names of the two sides matter not.

Infinite or one

A circle can take the shape of a polygon with n no of sides where length of the side tends to be smaller and smaller and with that value of n will reach infinity as the length approaches zero.

I hope this solves your question theoretically.

It will have 360 sides if your integral is one degree apart.

My old teacher asked me once what year was the War of 1812 fought in and I asked if this was multiple choice? So having said that I’m totally clueless on your question 😂

When you are in a circular room with the kids, and you really want to punish them. Tell them to stand in the corner.

It fucks them up! 🧐

Silly ... a square has 6 sides, left, right,top, bottom, front and back.

A cube has six sides as well.

A circle has no left, right, top or bottom, yet it does have a front and back. 2

A sphere though has no sides!

Circumscribe a cube around a sphere. Now spin the sphere in the cube. Like a gyroscope.

Where are the side's of the sphere in relation to the cube?

One. It is continuous . There no inside. It is closed

Well you’ve certainly stirred up controversy this morning? Proud of yourself? 😂

Inside and outside. How many is that? I am not good with numbers.

Infinite sides is the correct answer for once again.

2. Front and back? How many holes does a straw have?lol

Just one that's all over the place.

infinity numbers of sides....

the inside and the outside

All of them.

0
All parts of the circle are of equal distance to the center of a circle. A side must be comprised of a line and two angles, one on each side of the line.

If you plotted it on plane..Then there is an upper and lower.
It depends on how you play with the words
As a curve
Limit , etc

Inside and outside and other circle's have only one side 😚

circle has a ghanchakker associated ,,,, a typhoon.

Two — the inside and the outside.

Two!
How many sides does sphere has?

A circle has Infinite sides.

infinite sides.

360 .. 😜

2 - Inside and outside.

An upside and a downside.

0.

Sides in geometry are the stuff of polygons. A circle doesn't have any lines traveling between two fixed points. No sides.