River Sinuosity

Mathematicians have hypothesized that a river’s sinuosity (“how curvy” a river is in respect to its straight-line distance) averages out to pi.  That is, if you take all the rivers in the world and take the averages of their length to distance covered in a straight line, you would get around 3.14.  An example of how to calculate River Sinuosity is given below:

Screen Shot 2015-10-20 at 2.30.34 PM

Is this surprising?  Why might pi (which normally has to do with circles) find itself in river formations?


  1.  Write a one-sentence hypothesis as to why pi might appear in river sinuosity.
  2.  Watch the video embedded above.  Write a one-paragraph response as to why scientists feel that pi might be discovered in the ways rivers are formed?  Why is it only a hypothesis and not a certainty?
  3. Visit the website http://pimeariver.com/  Look at entry #64, our own Cumberland River.  Calculate the sinuosity of the Cumberland by dividing it’s length by distance covered (this information can be found in the graph on the right-hand side of the page).

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