404 Vocab: Math Terminology Not Found {Warning: Contains Really Awful Pun}

[tcepsa]

I 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"...)

Comments

[princesskaite.livejournal.com]

"any curve if extend will form a circle" is not a truism

There are arcs that never form a circle.

Your second point is valid tho if you say "Circle" instead of curve in the first instance.
For any given distance X along the Circle, the amount of curvature will be the same as any other portion of the circle having the same length." Hmm. That may have done it

More terminology and circle rule fun can be found: http://mathforum.org/library/drmath/sets/college_circles.html

Not true...

[elkor.livejournal.com]

An arc is, by definition, "Mathematics. A segment of a circle."

Re: Not true...

[(Anonymous)]

alrighty - then I picked the wrong vocab word. There are curves that never will form a circle.

I knew arc was pertinent somehow!

[elkor.livejournal.com]

"Any curve defined by exactly three points will, if extended a sufficient distance, form a circle."

W/ 2 pts, you have a line. While in a non-infinite universe it may eventually intersect itself, mathematically, it isn't precise.

w/ 4 points, you could define a hyperbola, which will never meet itself.

[blushing-grace.livejournal.com]

Until you make it curved so it cork-screws...

[elkor.livejournal.com]

3 points define a plane.

Therefor, any geometry that is constructed through exactly three points lies on a plane by default.

A corkscrew is not a planar geometrical feature, therefor requires more than 3 points to define.

[tcepsa.livejournal.com]

*nods* That works! ^_^