How many sides does a circle have?

Question

None of my teachers could ever give me a straight answer to this. My assumption is that you'll say one of the following:

zero
one
infinity

If you have an answer, please back it up with reasoning. Thank you very much!

...also... how many corners does a circle have?

Answer 1

A circle has an infinite number of sides, which means that it has an infinite number of courners as well. If you take one section of the circle, it will look curved. But as you zoom in, it will look less curved, and eventually you will have linearity. That is where the sides come from. As proof, look at a decagon (10 sides). It is starting to look round. As you add more and more sides to a polygon, it starts to look more and more like a circle. If you had a polygon with 1000 sides, would you be able to distinguish the different sides?

OR

A circle has an infinite number of tangent lines. If you drew every single tangent line, you will have a circle. Each tangent line is a side.

Answer 2

Actually, I did a rather good study of this (I was mainly studying n-gons, and their inscribed/circumscribed relationships with circles).

The number of "sides" of a circle is infinity. Or as close an approximation as the accuracy of your circle you can get. Consider:

A triangle is a 3-"sided" polygon (I'm going to talk of polygons in an equilateral sense where all side lengths and [obtuse] angles are equal). A square is a 4-sided figure. A pentagon is a 5-sided figure, a hexagon is a 6-sided figure, an octagon is an 8-sided figure (I forget what a 7-sider is offhand), a nonagon is a 9-sided figure. Notice how as you draw them the figure approaches a circular configuration. I posit and have in my studies basically shown than as the number of vertices of a perfectly equilateral n-gon (I don't know if that's the technical term; I just mean a ploygon with N sides and N vertices) increases so does its apparent similarity to a circle. So, the higher the number of sides, the more it looks like a circle. One could use a limit to say that as # of vertices -> infinity, the figure gets closer and closer to a circle. So we can pretty much say that a circle has infinite vertices if it's a "perfect circle." Otherwise it's simply an n-vertexed n-gon with arbitrary precision (IE an arbitrary number of vertices approximating a circle).

Of course as the number of vertices increases they get closer and closer together until they are essentially "continuous" rather than distinct. points.

There was actually a formula I got out of the equations I was using that was a great approximator precisely for this reason. You could basically specify the precision to which you wanted to computer a number and it would give you a number to that precision (beyond that precision the numbers were incorrect approximations).

Hope that all made sense. This was a perplexing one for me too, but after a bunch of geometric study it was pretty obvious what was going on. I might still have my binder around with my calculations in it. Ofcourse infinity is hard to work with. But there you have it. A "perfect" circle has infinitely many sides. Otherwise it's an arbitrarily large n-gon.

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Eulercrosser:

"To the people who say that it has infinite sides, where do you get your informations, a point is not a side."

You're right the point or vertex is not a side.

We get infinite sides from points because the line between any two points on the circle, no matter how infinitessimally small DOES exist. If we're assuming points are discrete / digital / quantized, whatever and there is a gap between them of the length 1/#ofpoints. You can keep subdividing and subdividing infinitely and still have an even smaller gap as you approach "infinity" or since infinity is basically just saying "without bound" we can say that the gap gets smaller and smaller "without bound". There's no smallest possible gap since any number can be divided by two to get a different number half the size. Of course it's all theoretical and imaginary... But hey... ;o] What's good for the goose is good for the gander.

Answer 3

Does A Circle Have Sides

Answer 4

There are two sources of ambiguity here.

The word CIRCLE sometimes refers to a circular disk (because it is common to talk about "the area of a circle"), but often the word refers only to the boundary of the disk (namely, the points that are equally distant from the point at the center of the figure).

The meaning of the word SIDE depends on its context. A polygon in the plane has, by definition, n vertices and each pair of consecutive vertices are joined by a side. It is clear that a polygon with n vertices has n sides. In general, the word side depends on the dimension of the figure -- a side is always part of the boundary.

So what is the side of a circle? If you think of the circle as a disk then it it has an up-side and a down-side. If you think of it as a curve, then it has an inside and an outside. If you think of it as the limit of an n-sided regular polygon, then one can justify the answer that the circle has infinitely many infinitesimal sides. Our conclusion:

the question, "How many sides does a circle have?", is too ambiguous to have a definite answer.
Perhaps the appropriate response is "there is no natural way of saying what the side of a circle is."

A circle difinately has 0 corners as the definition of a corner is :the point where two lines meet or intersect. A circle is of course ONE line.

Answer 5

The answer to your question depends on the geometric system that you are using and the point of reference.

In euclidian geometry, a circle is defined as the set of all points equidistant from a center in a plane.

Given that. The circle is a set of points, not a set of infinitely small sides. So in this case it is 0.

In non euclidian geometry, such as spherical geometry, the cirlce is defined by the line generated by the intersection of a plane with a sphere. In this case the number if sides depends on where it is viewed from. From the perspective perpendicular to the plane that defines the circle, the circle is a line. As such you can make the legitimate arguement that it is a 1 dimensional object which could be construed as a side in that system.

I won't bore you any more, but you really need a heck of a lot more information to answer such a deep question. For the assumptions you make will determine the answer that you get.

Answer 6

An inside and an outside.

Intrinsicly, each of the atoms that make up the boundary of the circle become a corner. When folks like Pythagoras discovered that the perfect geometrical form, a circle, had an irrational number, pi, that was a constant factor in the dimensions of the circle, they thought it a fact too strange for the world to hear. It becomes an almost infinite number of points that define the curve of the circle, those points are therefore corners of that infinitely-numbered pieces of boundry lines.

Answer 7

It has infinite sides and thus corners.

The reason is almost same as q2003 that if u look closely into the circle ie zoom, u will look that it is in actual the point at any point and the sum of those points/dots constitutes the circle.

And u cant count dots because they number up to infinite.

Second, way to checking the side is by drawing the tangent to any point and u will notice that the angle from the centre will be different unlike if u do the same with rectangle of square thus it has infinite sides!

I think it answers!

Answer 8

To answer your question as asked.
"How many sides does a circle have?"
Two sides.
My reasoning is basic.
The inside and the outer side.
Try as you might, you can't fault this answer.

Now, corners is a different story,
By loose definition and slight manipulation, the word converge, it could be said, " in order to form a circle, a line drawn in a circular motion from end to end would "converge" creating a circle.
Corner, by definition is the meeting of two converging lines or surfaces.
Alas the answer would be, one
All in good fun.

Answer 9

The answer to this Question is infinite because since the circle is spherical two dimensional figure without any corners every on circle can be considered as a side
And there are ifinite points on the circle we have infinite sides

Answer 10

The question, "How many sides does a circle have?", is too ambiguous to have a definite answer. Perhaps the best answer is there can be more than one answer...the most logical one would be zero or infinite.