River Paths

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As a follow-up to this recent post about river meander, check out this video from Numberphile about some of the mathematics behind the path of rivers. A river’s course is typically much longer than the direct distance between its origin and outlet; the ratio of these two distances is the river’s sinuosity. The fluid dynamics of a river’s bend tend to create stronger bends, but, once a bend reaches an extreme point, it will often be cut off, thereby straightening the river’s path. A model of unconstrained rivers suggests that, on average, the sinuosity of rivers should be about pi. As noted in the video, it would be very interesting to see how this theory holds up next to real rivers. But, given the way humans have fixed the course of rivers to prevent flooding, their current sinuosity is probably far from natural or unconstrained. (Video credit: Numberphile; research credit: H. Stølum; submitted by haxpaxmax)

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