Rivers and pi

I clearly recall being told by a geography teacher at school that all natural, mature rivers in their floodplain (ie lower reaches) are 3.14 etc times as long as the direct distance between where they enter the plain and the sea (or lake). In other words, the total distance that they travel is pi times the straight-line distance.

I have been unable to find any corroboration of this (potentially) beautiful idea. Does anyone know anything of this?

via International Skeptics Forum http://ift.tt/1Ho8VBr