meander curve

For the meander curve the curvature is linear related to the sine of the arc length s.

Luna Leopold and W.B. Langbein used the curve to approximate the sinuosity of river channels ¹⁾.
The characteristic repeating pattern of a rive is called a 'meander', what leads to the name of meander curve. The sine relationship led to the name of the sine-generated curve.

It appears that this meander curve has the smallest variation of changes of direction, in comparison to other curves with a meander-like form.

When you hold a thin strip of spring steel firmly at two points, and allow the length between those points to assume an unconstrained shape, the same curve form results.

Pictures:

notes

1) Scientific American of June 1966