# Talk:Circle

why the formula for circumference is expressed as 2pi r rather than simply pi d? Anyone know?

Well, it sometimes *is* expressed as πD.

I'm just guessing here, but I think the radius is considered a more fundamental parameter for a circle than the diameter. The circle is the set of points that is all the same distance from a central point, and that distance is the radius. (There are, incidentally, many shapes other than the circle that have a constant *diameter,* but only the circle has a constant *radius...*).

Of course, that just changes the question: why was the symbol π defined as referring to the ratio of circumference to diameter, rather than the ratio of circumference to radius, 6.28... It really should have been; when you think of it, it is really the value 2π that keeps cropping up everywhere. Dpbsmith 15:28, 24 April 2007 (EDT)

- Agree with Dpbsmith - the radius is essentially part of the definition of a circle (the locus of all points...). In other words, working with abstractions one is more likely to have
*r*defined than*d*. Perhaps the article should list both for clarity - and mention that this is the*definition*of pi. And, you're right,. We should bring this to the attention of the authorities. Human 15:59, 24 April 2007 (EDT)**pi should be 6.28318... !!!**

- The Greeks defined pi to be the ratio of the area to the radius of the unit circle. That's why it came out 3.14... instead of 6.28... . I just edited the page to correct some slight mis-statements (the circumfrence is not a line because a line is by definition straight in Euclidean geometry), but it isn't worded well. Please fix the wording.
- I don't see any problem with your wording, looked clear to me. Good point about the Greek definition of pi. And thanks for fixing my silly "origin-centered" formula for a circle! Human 22:12, 7 May 2007 (EDT)

- The Greeks defined pi to be the ratio of the area to the radius of the unit circle. That's why it came out 3.14... instead of 6.28... . I just edited the page to correct some slight mis-statements (the circumfrence is not a line because a line is by definition straight in Euclidean geometry), but it isn't worded well. Please fix the wording.