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September 19th, 2014, 11:19 AM   #1
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"sides" of a circle

Yesterday someone asked me the following question. I could not really answer it.

How many sides does a circle have?

I thought about it carefully at home. I concluded that it had no sides. Later, I thought about it again and got a different conclusion. I think the circumference of a circle counts as a side. I am not exactly sure.

Can someone explain how many sides a circle has? Thanks.
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September 19th, 2014, 11:32 AM   #2
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To have a side, at least two points are required. If someone asks generally, how many sides a circle has, the answer would be none. But this is also a fact that a circle has infinitely many points on it. One may conclude that a circle has infinite number of sides. So, this question has contradictory answers. Suit yourself with the answers. Answering generally, I would say a circle has no sides (elementary point of view).

Last edited by Prakhar; September 19th, 2014 at 12:13 PM.
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September 19th, 2014, 12:12 PM   #3
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Quote:
Originally Posted by davedave View Post
Yesterday someone asked me the following question. I could not really answer it.

How many sides does a circle have?

I thought about it carefully at home. I concluded that it had no sides. Later, I thought about it again and got a different conclusion. I think the circumference of a circle counts as a side. I am not exactly sure.

Can someone explain how many sides a circle has? Thanks.
A circle can be thought of as the limit of a sequence of regular polygons as the number of sides increases to infinity. So a circle has an infinite number of sides of infinitesimal length.
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September 19th, 2014, 01:01 PM   #4
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That really means "none". When we are talking about polygons, it is clear that a side is straight, a circle has no straight lines (it's not a polygon). The limit doesn't have to be an actual value in the sequence being taken to that limit, and frequently isn't.

If we are not talking about polygons, anything goes for boundary lines. So you have to define what you mean by a side. A reasonable definition might be "a continuous smooth curve" in which case a circle has one.

The bottom line is that you need to define your terms before attempting to answer the question.
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September 19th, 2014, 02:45 PM   #5
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Hello, davedave!

Quote:
Yesterday someone asked me the following question.

How many sides does a circle have?

Did that 'someone' have a smirk on his/her face?

This is a classic children's riddle.

Answer: two sides . . . inside and outside.

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September 19th, 2014, 04:33 PM   #6
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Originally Posted by soroban View Post
Answer: two sides . . . inside and outside.
However, if you're inside, you'll go nuts trying
to find a corner to pee in

Last edited by Denis; September 19th, 2014 at 04:36 PM.
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September 19th, 2014, 05:32 PM   #7
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Quote:
Originally Posted by RyanPowers View Post
A circle can be thought of as the limit of a sequence of regular polygons as the number of sides increases to infinity. So a circle has an infinite number of sides of infinitesimal length.
Beautiful.
It's one of those definitions that can awaken one's appreciation for mathematics. It's like porn, once you've been exposed to it you can't get enough of it.

A man's mind stretched by a new idea can never go back to it's original dimensions (Oliver Wendel Holmes).
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September 20th, 2014, 08:18 AM   #8
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Quote:
Originally Posted by RyanPowers View Post
A circle can be thought of as the limit of a sequence of regular polygons as the number of sides increases to infinity. So a circle has an infinite number of sides of infinitesimal length.
But shouldn't a side be a straight line that has 2 points (the end points) and "surrounds" a shape?

The definition of a circle is "set of points in a plane equally distanced from one point which is called the center". We cannot draw a "tangent" to the side of the circle, or a line that passes through the side of the circle, only to one point. Therefore circle has no sides.
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September 20th, 2014, 10:23 AM   #9
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Originally Posted by jonah View Post
It's one of those definitions that can awaken one's appreciation for mathematics.
My bad. I should have instead posted "It's one of those concepts/ideas that can awaken one's appreciation for mathematics."
My excuse: Mixing beer and gin.
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September 20th, 2014, 11:21 AM   #10
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Quote:
Originally Posted by soroban View Post
Hello, davedave!


Did that 'someone' have a smirk on his/her face?

This is a classic children's riddle.

Answer: two sides . . . inside and outside.

Are you trying to say that a triangle has 5 sides, three line segments and one inner side and one outer ? Or a square has 6 ? Inner side and outer side concept is true but not in this case. Here, as posted by others too, a side is defined as : A line that makes a perfectly flat, but two-dimensional shape.
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