helix
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By integration. Divide the curve into small pieces, then add up the length of all the pieces.
elipse
yes but the figure is a closed curve. The distance around an object is the perimeter.
Technically yes; a curve with infinite radius.Technically yes; a curve with infinite radius.Technically yes; a curve with infinite radius.Technically yes; a curve with infinite radius.
The gradient of the tangents to the curve.