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How Many Sides Does a Circle Have?

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The answer to ‘How Many Sides Does a Circle Have’ is not as simple as one might expect it to be. Depending on the mathematical sophistication of the person you ask this question, you will come across different answers like zero, one, or infinity. 

A school teacher might expect a different answer from her students than what an academic trained in mathematics might give. To simplify this conundrum, we walk you through all the possible answers and explain the reasoning given by those in favour of those answers. 

If you are a parent, you might probably want to stick to what the teacher expects, but at the same time, you might also want to introduce your child to what advanced students of mathematics think to develop them intellectually.

All that said, let’s go through all three possible answers and the justifications for them, one by one. 

Answer 1: Zero 

In schools, a common question asked to young students in their earlier grades is this: 

If a triangle has 3 sides and a rectangle has 4 sides, how many sides does a circle have?

Students are also often shown visual representations of triangles, rectangles, and circles along with this question. Many students often lean towards saying that a circle has zero sides because they contrast the straight sides of triangles and rectangles with the circle. 

The answer given by these students is intuitive, and they unconsciously end up defining sides as ‘straight lines’ when arriving at this answer. Most school teachers also expect this answer from students.

Answer 2: One

While zero is the right answer if you define a side as a straight line, you can also say that a circle has one side if you allow the definition of side to include a curved line. 

Even though this answer can be correct if you consider the aforementioned definition, this is not a popular answer even among school teachers.

Answer 3: Infinity

Infinity is the answer you will find advanced students of mathematics leaning towards. However, it is not easy to grasp how a circle can have infinite sides on a first glance of the circle, so let us try to understand it visually with a few examples. 

Imagine you put a triangle in a circle like in the image below:

Triangle Inside A Circle ( How Many Sides Does A Circle Have )

You can see that the triangle is not exactly matching the circle because the yellow shows through. 

But if you put a square in, you will notice that there’s a little bit less of the yellow left like in the image below.

Square Inside A Circle ( How Many Sides Does A Circle Have )

You will see even lesser yellow if you put a hexagon inside the circle like in the image below. 

Hexagon Inside A Circle ( How Many Sides Does A Circle Have )

If you put a polygon that has 50 sides and is of the same size as the original circle on top of the yellow circle, the original circle will not be visible at all. 

Polygon Inside A Circle ( How Many Sides Does A Circle Have )

Now, the polygon above has 50 sides and is almost exactly the size of the circle, which also means that the bigger the number of sides you have, the closer you are to a circle. By this logic, the number of sides a circle has are infinite.

A cirlce has infinite sides

To sum it up, the answer to how many sides does a circle have depends on who you ask the questions. While school teachers are more likely to accept zero as the answer, mathematicians mostly consider infinity the correct answer. 

Note: Images in this article have been sourced from here.

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How Many Sides Does a Circle Have?
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The answer to ‘How Many Sides Does a Circle Have’ is not as simple as one might expect it to be. Depending on the mathematical sophistication of the person you ask this question, you will come across different answers like zero, one, or infinity. 
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AllThingsStatistics

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