0, 1, 2, Or Infinite: How Many Sides Does A Circle Have?

“How was your day at school?”

“Nearly perfect if it weren’t for a circle that kept me thinking all the way home.”

“Isn’t that the circle of the red zero written in your notebook?”

“Maybe, if I continue to be unable to find an answer to the question ‘How many sides does a circle have‘!”

If your child said that, what would you think? The question is too simple, it’s as easy as pie to answer it, right? So what’s your answer? Do you believe that you will be confused and want to change the original answer when I give the 4 options below and the explanations attached? Scroll down and let these numbers prove what I just said.

0

Let’s start with a popular answer: A circle is not a sided plane shape. Why?

No matter how infinitely small the angle of 2 radiuses forming a chord at 2 points on the arc is, it is still bounded by a curve. As a result, it’s more appropriate to call a circle a border of a uniform curve.

1

0 seems to be the answer that got a tick, but if you keep repeating terms like “chord”, “arc”, or “curve”… to a 5-year-old just learning to count, then they will cry!

In primary school, it appears that “1” is the correct answer. A reasonable cause for it is based on one meaning of the word “side” definition. Some argue that the side is part of a line, and if we are not insisting on the line’s straightness, it’s evident that a circle has one side. 

How many sides does a circle have? - A polygon of infinite sides
How many sides does a circle have? – Photo from www.pinclipart.com 

 Here is another support for the answer “1” (it’s more complicated than what a 6-year-old kid can understand, so please don’t make him scream while reading!). If you mean by “circle” its circumference along with its interior, then that circumference is its border. We can say border as a side, and in that case, a circle has 1 side.

2

Now consider another definition of the word “side”. Side is an area just beyond the edge of something. A circle is a line that extends indefinitely. Every line has only 2 sides. As a result, the circle has 2 sides. 

Infinitely Many

How many sides does a circle have?‘ “Infinitely many!” Seems to be a safe bet made by many people, but is a circle a polygon? Does a circle have an unlimited number of sides?

Obviously, many people consider a circle a polygon with the number of sides getting larger and larger and reaching infinity. This is precisely the method that Archimedes, Liu Hui, and numerous other mathematicians used to calculate π.

It’s pretty reasonable to conclude a circle is a polygon having an unlimited number of sides at times. In this case, every point in a circle is the vertex of a circle.

However, each side has a length of…zero? In my opinion, sides of zero length are a difficult notion to grasp. Assume I’m analyzing a square, making it appear as a hexagon like this illustration:

How many sides does a square have? - Lengths of zero
How many sides does a square have? – Photo from richardelwes.co.uk

So how many sides does a square have? 4, 8, or infinite? 

So it will make sense for us to think of my square as having 8 sides, 4 of which have length 0! Sound weird, right?

Many people consider a circle a polygon with the number of sides getting larger and larger and reaching infinity
So how many sides does a circle have? – Photo from www.reference.com

The Right Answer For ‘How Many Sides Does A Circle Have’

Okay, so in short, if you encounter a multiple choice question ‘How many sides does a circle have’, which answer would you tick? Or will you wipe the beads of sweat from your forehead and tick 1 option randomly because each all makes sense?

Answering the question ‘How many sides does a circle have’ seems as simple as an easy counting activity, but it is just as confusing as counting sheep when you are slowly falling asleep.

The complexity of this question boils down to the fact that the word “side” has so many meanings! Is it an edge, part of a line, or an area bounded by the line?

In this situation, a good teacher wouldn’t puzzle students with such a multi-meaning word. They need to explain the meaning of the question clearly. So if your kid asks you this question, send this post to your kid’s teacher.

Interested in “how many” and “how much” questions like the ‘How many sides does a circle have’? Then our Science Archives section is for you. Visit Jobandedu for more.

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