From Numberphile: “Sinuosity is a measure of how ‘bendy’ a river is. It is the length of the river divided by the direct route. Featuring Dr. James Grime.”
Update
After posting this video, Dr. Grimes and Lawrence Roberts began collecting and analyzing data about real-world rivers. It turns out the pi theory of sinuosity is too simple. Read about their results:
Denise Gaskins' Let's Play Math 
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