Do you object violently to the description of "straight" for some reason? — apokrisis
If something is not bent, what is it? If something is not twisted, what is it? If something is not curved, what is it? — apokrisis
So do you agree that "straight" is routinely understood as being the antonym of these various forms of crookedness - "bent", "twisted", or "curved"? They are all ways of asserting "not straight"? — apokrisis
The rest of my argument follows of course, so no need to repeat it. — apokrisis
No, I don't agree. — Metaphysician Undercover
All those words have a particular meaning, referring to a particular shape. — Metaphysician Undercover
Great. And what particular shape does each of those particular words refer to then?
Curved = ?
Bent = ?
Twisted = ? — apokrisis
None is the opposite of straight. — Metaphysician Undercover
Curve = "...having a regular deviation from being straight or flat, — Metaphysician Undercover
As I said, it's very useful for determining the different ways in which the thing being measured varies from the standard of measurement, but the straight ruler wont tell you why the thing you are trying to measure is crooked. Nor will you get an accurate measurement of the crooked thing using the straight ruler. That's why we must devise other means for measurement. But first we must figure out why the straight ruler is not giving an accurate measurement. — Metaphysician Undercover
Nor will you get an accurate measurement of the crooked thing using the straight ruler. — Metaphysician Undercover
This is what then doesn't make sense. If the crooked is the not straight (in some degree), then only something straight could be used to measure the degree of that non-straightness. — apokrisis
Intuitively, curvature is the amount by which a geometric object such as a surface deviates from being a flat plane, or a curve from being straight as in the case of a line.
https://en.m.wikipedia.org/wiki/Curvature
Why use the reciprocal in defining curvature? It is natural for the curvature of a straight line to be zero. Imagine straightening out a curve making it into a straight line. In the limit the circle of best fit has infinite radius giving zero curvature.
https://nrich.maths.org/5654
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