Proof of calculating area and volume

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The discussion centers on the mathematical definitions and calculations of area and volume for geometric shapes, particularly circles and spheres. It emphasizes that while the formulas for perimeter and area arise from integration, there are intuitive proofs that can be understood without advanced calculus. A key point of contention is the distinction between a circle, which is a one-dimensional curve with zero area, and the disk, which is the two-dimensional area enclosed by the circle. Participants debate the terminology and definitions, asserting that the area of a circle is often mistakenly referred to, when it should be the area of a disk. The conversation highlights the importance of precise language in mathematics to avoid misconceptions.
  • #31
Rogerio said:
Who is misleading people here?

According to you, if circle was just a curve, its area would be zero.

However, try google "area of a circle" and "area of a circumference", and see the difference. If it is not enough, google "area of a disk", too.

I find your arguments to be funny... :-p Sad but true... :-p

The circle is a curve.It has null area.It encloses a plain domain called DISK.

Daniel.
 
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  • #32
Rogerio said:
Who is misleading people here?

According to you, if circle was just a curve, its area would be zero.

However, try google "area of a circle" and "area of a circumference", and see the difference. If it is not enough, google "area of a disk", too.

"Circumference" is a number, not a set of points. The correct term for the set of points equi-distant from a given point is "circle" it has a circumference but its area is 0. The correct term for a the set of points bounded by a circle is "disk". It has non-zero area.

I did google on the terms you suggested. Of course, it is common to talk about the "area of a circle" when the strictly correct phrase should be "area of a disk". I notice that the hits on "area of a circumference" (there were only 4 as compared with thousands for "area of a circle" and "area of a disk") are all translations from a non-English source. I suspect that "circumference" is a mistranslation.
 

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