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Comments on How do mathematicians measure shape perimeters?

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How do mathematicians measure shape perimeters?

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When I create a circle on a computerized plane with a graphic editing program (such as Window's Paint), I can see a group of dots circling around an imagined central point.

if the perimeter is comprised of just one layer of dots we could always add another layer of dots on top of that first layer, and then a third one on top of the second layer, and so forth.
In CSS code it might be: border: 1px solid black and then 2px and then 3px.

In classical mathematics, how do mathematicians set or measure the perimeters (border thickness) of circles and other shapes that they draw on paper, or in a more daily life manner, if one has a pipe with the diameter of 3cm, how could that person measure its perimeter (circumference)?

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2 comment threads

"Thickness," not length of perimeter (4 comments)
Using formulae? (5 comments)
Using formulae?
Moshi‭ wrote over 3 years ago

Are you looking for an answer other than "The perimeter of a circle is given by $2\pi r$"? Because most common shapes already have formulas for their perimeter. (And for arbitrary parameterized shapes you can just use a line integral, which is basically another fomula)

deleted user wrote over 3 years ago · edited over 3 years ago

Hello Moshi, thank you, sadly I don't know what are the Greek letters there and can't copy-paste what you wrote there to learn about it because it's an image. I don't know what a "formula for a perimeter" mean besides in computing when I do for example border: 2px solid black so I know that the perimeter would be 2px large.

Moshi‭ wrote over 3 years ago

deleted user When you do border: 2px solid black, you make it 2px thick. The length of the perimeter would not be 2px.

The Greek letter there is pi, https://en.wikipedia.org/wiki/Pi

deleted user wrote over 3 years ago

Moshi‭i, thanks, I understand any circle to be the border of the disk, so if that border got 2 px thickness, won't it be correct that the circle's perimeter is 2px thick?

Moshi‭ wrote over 3 years ago

deleted user Mathematical perimeters do not have a concept of width, since they are one dimensional. What you're describing is an annulus.