Mathematical Question || Is a Circle a Polygon?

[Oasis]

uh, no, it doesn't have sides

1 lined*

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[Ash]

A circle is indeed a polygon.

Define: Polygon

• A closed shape with more than two sides

Define: Side

• A straight line with a non-zero length

Define: Line

• The path between two points

Define: Point

• An instance in space

A circle is said to have an infinite number of sides.

With that logic, the sides have zero length.

Because of this, a circle is not a polygon.

But wait. If all of the sides have zero length, then how is it possible for the circle to have a non-zero circumference?

A circle does not have an infinite number of sides, instead, it has tons and tons of lines.

Technically, a triangle is a very low quality circle. An octagon is closer, but not quite.

The more sides you add the closer to a circle you get. This is where the "infinite amount of lines" idea come from. Of course, there is a limit. There will come a point in time where adding another side does not change the appearance of the shape. At this point, you have achieved a circle.

As the resolution increases, so does the amount of sides required. But even our eyes can only register a certain amount of lines. Otherwise, we would see particles and atoms. The only way to that a circle would require an infinite number of lines would be at an infinite resolution. Seeing as the ladder cannot exist, neither can the former.

[Iban]

Uh, no, a circle is not "tons and tons of lines."

A circle is one line.

It's path happens to be a perfect circle.

[Oasis]

Uh, no, a circle is not "tons and tons of lines."

A circle is one line.

It's path happens to be a perfect circle.

What I was trying to say.

[ECrownofFire]

A circle is defined as an infinite number of POINTS that are equally distant from one point (that distance is the radius, by the way). Therefore, it has no sides.

[Gamefandan]

So sides cannot be curved? Bullstuff.

[Otis Da HousKat]

The question in this thread was answered by the first sentence in the Wikipedia article for polygon. ._.

So sides cannot be curved? Bullstuff.

A "curved side" is called an arc.

[Wedge]

The question in this thread was answered by the first sentence in the Wikipedia article for polygon. ._.
A "curved side" is called an arc.

Exactly this, I basically pulled my response from Wikipedia. A circle has no sides. A curve is not a line, nor is it made up of small lines. You cannot construct an arc or any other kind of curve out of lines because then it is no longer a curve, it is a series of line segments that approximate a curve. A line of zero length is not a line, and using lines of "infinitely small size" does not work because they are still not curves, they are lines. You do not get a circle, you get an approximation of a circle using immeasurably tiny lines that are still lines.

Technically, a triangle is a very low quality circle. An octagon is closer, but not quite.

A triangle is not a low quality circle. That's like rounding 3.5 to 4 and then calling 4 a "low quality 3.5." It's not a low quality 3.5, nor does 4 equal 3.5.

[Ladios]

A circle is said to have an infinite number of sides.

NO
NO NO NO NO NO NO NO NO

That is an entirely different mathematical concept. You are wrong. Stop it.