Consider a smooth, 2-d plane curve of given fixed length $d$. Any straight line of length $d$, is also a curve of this type. What i am interested in is, How straight a curve of a fixed length, is? In terms of a mathematical measure. For example the straightness measure of a straight line of length $d$, is greater than the measure of any other smooth curve of length $d$. This measure intuitively, should be independent of the orientation or location of the curve in the plane. Basically shift invariant and rotation invariant.
2026-03-30 22:14:19.1774908859
Straightness measure for smooth 2-d plane curves of a given fixed length
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You want
to be straighter than 
even though the former turns 360 degrees and the latter only turns 90 degrees. The average inverse curvature is not really what you want since a straight line and a line with a single sharp bend (L) are both "straight" in this sense. Instead, why not use the inverse average distance (or average inverse distance) between the curve and the line joining its endpoints?