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tcepsaI had a thought a few seconds ago that I wanted to put in here, but I wanted to make sure that I was accurate about it. Then I realized that I didn't really know how to express it. Originally, I was going to write that "Any curve, if extended, will make a circle," but then I realized that I wasn't familiar enough with the term "curve" to be able to say that. And then I realized that I didn't know enough to say it any other way, either. "Uniform curve" seems the next best way of putting it, but even then I'm not sure that it's right. Of course, when I actually figure out what I want to say, it's basically going to probably end up being "Any curve that forms a circle if it is continued will, if continued, form a circle." But that's no good because it is a circular argument! (Hey, I warned you...)
What I'm wondering now is whether there is a way of describing a curve with words that says "For any given distance X along the curve, the amount of curvature will be the same as any other portion of the curve having the same length." Hmm. That may have done it (though I may be playing fast and loose with the term "curvature"...)
What I'm wondering now is whether there is a way of describing a curve with words that says "For any given distance X along the curve, the amount of curvature will be the same as any other portion of the curve having the same length." Hmm. That may have done it (though I may be playing fast and loose with the term "curvature"...)
