The discussion revolves around the definition of the circumference of a circle, specifically comparing the expressions \(2\pi\) and \(2\pi r\). Participants explore the context in which each expression is applicable, particularly in relation to the unit circle and circles of different radii.
Participants express differing views on the definitions of circumference, with some agreeing that both expressions can be correct under specific conditions, while others emphasize the importance of context in understanding the terms.
The discussion highlights the dependence on the definition of the radius and the specific context of the unit circle versus circles of arbitrary radius. There is an unresolved aspect regarding the clarity of the definitions in the referenced textbook.
Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?Shafia Zahin said:I just have a little question that i have read in the book of Thomas/Finney Calculus 9th edition that the circumference of a circle is 2pi,i can be wrong obviously but wasn't it supposed to be 2*pi*radius of the circle?
Please help.
berkeman said:Both are correct if the radius r = 1. Can you scan the page in question and UPLOAD it?
Math_QED said:Most likely, they calculated the length of the curve ##y = \sqrt{1 - x^2}##. This is the unit circle with radius ##1## and thus the circumference is equal to ##2\pi##.
If they would have calculated the length of the curve ##y = \sqrt{r^2 - x^2}##, the circumference would be equal to ##2\pi r##. This is the circle through the origin with radius ##r##.