What is the length of a circle called ?

[milanmajumder15]

What is the Length of a Circle called ?

1) Circumference or
2) Diameter

and Why ?

I am very confused by this question. According to my own understanding, length is a one-dimensional property of an object. But nowhere on the web, i could find this kind of definition. First of all, what is the proper definition of Length, and how can I find it?
And the main part of my question is, What is the length of a circle? is it its diameter or circumference? most people say circumference. But how? Circumference is neither its 1D property nor its distance between one end to another end.

I need to understand it deeply. Please Help me.

 

[Otis]

Hi. Length is distance, from a starting point to an ending point.

My driveway has length, yet it's not straight. However, I understand how "length of a circle" could be ambigous. Perhaps, that author had unrolled the circle (in their mind) such that its circumference became a straight line. If not, we can think of a point traveling around the circle's boundary until it arrives where it started. The distance traveled is the length of the circle's circumference, or just circumference, for short (the word 'circumference' may refer to a circle's boundary or the linear distance around it, depending on context).

Otherwise, I don't recall "length of a circle" defined, but I do remember "perimeter" used instead of circumference. Also, I've heard diameter described as a "circle's width".

EDIT: I searched "length of circle" and found that Wikipedia describes circumference as the arclength of a circle. So, there's two alternative wordings: circle's linear length or circle's arclength.
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[Steven G]

The length of the circumference is most certainly 1D.
I have a multiple choice question for you.
1st imagine I drew a circle on this page.
Question: What is the length of the circle?
1) 2 in²
2) 3 ft³
3) 9
4) 17 inches.

Which would you pick?

For the record, choice 1 is an area (2D), choice 2 is a volume (3D), choice 3 has no units and choice 4 is a length (1D)

 

[Otis]

The length of the circumference is most certainly 1D

The exercise doesn't ask for "the length of the circumference".
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[milanmajumder15]

I have uploaded the source for you. I have also read your answer but I still don't know how to handle this situation. If you say circumference is the length of the circle's perimeter then it's ok. but I think the length of the circle should be its diameter. I don't know what's wrong with my intuition.

 

[Dr.Peterson]

I have uploaded the source for you. I have also read your answer but I still don't know how to handle this situation. If you say circumference is the length of the circle's perimeter then it's ok. but I think the length of the circle should be its diameter. I don't know what's wrong with my intuition.

The book clearly says they are using "the length of the circle" to mean its circumference, and that this is measured "along the circle". Why would you take it any other way?

Language can be ambiguous, and doesn't always mean what we expect it to mean. When we are given a definition, we use that, rather than our intuition. In this case, their clarification definitely overrides any other considerations.

 

[Otis]

I think the length of the circle should be its diameter. I don't know what's wrong with my intuition.

One issue is that the phrase "length of the circle" is ambiguous.

If I see a circle drawn with a horizontal diameter, then "circle's width" seems natural for the length of that diameter.

If I see a circle drawn with a vertical diameter, then "circle's height" seems natural for the length of that diameter.

There's no diameter orientation (for me) where it would be natural to say "circle's length".

Perhaps, in your mind, the horizontal view is 'length" not 'width'. For example, I'd say a bookshelf is 3 meters wide. Would you say it's 3 meters long?

Aside: When I see a random, unlabeled, non-square rectangle, I naturally pick 'length' for the longer side and 'width' for the shorter side. I'm not sure why because in such situations the labels don't matter. Each of us has personal preferences; sometimes, we need to adjust a preference because everybody else is doing the thing differently, heh.
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