Question about circumference

TheAngryHulk

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I know this might sound strange but, if you cut a circle in one specific spot and straightened it into a line it would have a length. Why isn't that length considered the circumference?
 
I know this might sound strange but, if you cut a circle in one specific spot and straightened it into a line it would have a length. Why isn't that length considered the circumference?

1) line SEGMENT
2) Definition. A circumference must enclose something.
3) Sometimes, the circumference may refer to the linear distance only, and not the locus of points so measured.
4) If your construction is a circumference, can you define what it encloses?
 
1) line SEGMENT
2) Definition. A circumference must enclose something.
3) Sometimes, the circumference may refer to the linear distance only, and not the locus of points so measured.
4) If your construction is a circumference, can you define what it encloses?

"The locus of points" is the circle, not the circumference. The circumference is a measure of length.
 
I know this might sound strange but, if you cut a circle in one specific spot and straightened it into a line it would have a length. Why isn't that length considered the circumference?
The circumference, being a length, is linear; ie it can be measured against a ruler. So yes, if you cut a string that is in the form of a circle and placed the string against a ruler it would be the length of the circumference--By Definition of circumference! Why do you thing otherwise?
 
"The locus of points" is the circle, not the circumference. The circumference is a measure of length.

I stand by #3. "Circumference" can be either the distance around something, not necessarily a circle, or the enclosing boundary itself.
 
I know this might sound strange but, if you cut a circle in one specific spot and straightened it into a line it would have a length. Why isn't that length considered the circumference?

in a way it is.
the length you describe will have the same measurement as the circumference.
 
The circumference, being a length, is linear; ie it can be measured against a ruler. So yes, if you cut a string that is in the form of a circle and placed the string against a ruler it would be the length of the circumference--By Definition of circumference! Why do you think otherwise?


First I didn't know circumference was considered a measure of length. Second I couldn't understand why pi has to be part of the formula.
 
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