The meanderiness of a river, its Stølum number, is... - Maths and Science blog- matthen - http://blog.matthen.com/post...
"The meanderiness of a river, its Stølum number, is defined as the length the water travels from source to finish (blue curve) divided by the direct distance (red line).  This can change chaotically as a river changes coarse, forming Ox bow lakes. The ratio is often found to converge to (but rarely exceed) 3.14, roughly pi." - Amit Patel
(animated gif - click through to see) - Amit Patel
Why would this converge to pi?! - Amit Patel
I guess the courses of rivers tend to approximate alternating half-circles with the straight-line distance as the diameter? - Victor Ganata
Hm, that makes sense! :) - Amit Patel