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One surprising thing we found out about Pi this week is that Pi can also describe the bendiness of a river. Is this a tall tale, or another example of this astounding constant in everyday life.
A river’s bendiness is described by is sinuosity, a number which indicates how meandering a river is based on the actual length of the river and it’s “as the crow flies” length. It turns out the average river has a sinuosity of about 3.14. So where did this fact come from?
In the 1990s, Professor Hans-Henrik Stoulum, a scientist from Cambridge University, calculated the ratio between the actual length of a river from source to mouth, and their straight-line length. He found that most rivers had a sinuosity of just above 3. Based on your knowledge of Pi, and the shape of the earth, why do you think that this number would be seen when looking at the sinuosity of a river.
“Einstein was the first to suggest that rivers have a tendency toward an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which will in turn result in more erosion and a sharper bend. The sharper the bend, the faster the currents on the outer edge, the more the erosion, the more the river will twist, and so on. However, there is a natural process that will curtail the chaos: increasing loopiness will result in rivers doubling back on themselves and effectively short-circuiting. The river will become straighter and the loop will be left to one side, forming an oxbow lake. The balance between these two opposing factors leads to an average ratio of Pi between the actual length and the direct distance between source and mouth” (Singh, 1997). This video provides a useful visual to the meandering erosion of rivers (Discovery Education Streaming, Science Techbook, Social Studies Techbook | Canadian Link)
However, rivers are rarely left to develop their own course, and they can be constrained by natural boulders, valleys, and vegetation. What impact do you think this has on the average sinuosity of a river?
Why not have students try this for themselves? Working with a partner, each create a drawing of a river. It can be as bendy or as straight as they like, it just needs to reflect the shape a river can have in the real-world. Have students swap drawings and calculate the ratio of the real length to that of it’s “as the crow flies” length. (Some string might be useful here). Share the results as a class – and don’t forget to let us know how you get on, you can share via Twitter and Facebook.