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, pi should be 6.28318... !!!. We should bring this to the attention of the authorities. Human 15:59, 24 April 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.