Is the average sinuosity of the world's rivers equal to pi?
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Re: Is the average sinuosity of the world's rivers equal to pi?
#2It would be nice if the distribution graphic of the sinuosity has units.
Also, there is a clear outlier with sinuosity 7.6. Which river is it?
Re: Is the average sinuosity of the world's rivers equal to pi?
#3It would be nice if the distribution graphic of the sinuosity has units. Also, there is a clear outlier with sinuosity 7.6. Which river is it?
The Lukuga -- #40 on the list.
I suspect there is an error in the data. The project lists the Lukuga River as being 1904 km long. But Wikipedia[1] only has 320 km, which would give it a much more ordinary sinuosity of 1.27.
For a river that might actually have a very high sinuosity, take a look at the Fraser River -- #20 on the list, with sinuosity listed as 5.12.
Re: Is the average sinuosity of the world's rivers equal to pi?
#4Great project! Seems like one could scrape the data from Wikipedia. I entered a few rivers by just copying data out of the Wikipedia side bars for them. Any reason that wasn't done?
Re: Is the average sinuosity of the world's rivers equal to pi?
#5Do rivers actually have a well-defined length? I know coastlines do not, and rivers seem similar.
Re: Is the average sinuosity of the world's rivers equal to pi?
#6I guess the answer is no.
Re: Is the average sinuosity of the world's rivers equal to pi?
#7Do rivers actually have a well-defined length? I know coastlines do not, and rivers seem similar. https://en.wikipedia.org/wiki/Coastline_paradox
The complexities there don't seem to have a correlary to the rivers.
Re: Is the average sinuosity of the world's rivers equal to pi?
#8Do rivers actually have a well-defined length? I know coastlines do not, and rivers seem similar. https://en.wikipedia.org/wiki/Coastline_paradox
Yes.
With a coastline, the closer you measure, the more length-increasing features you observe, causing the measured length to diverge.
Rivers have a finite width, so once the distance between your measurements is smaller than the width of the river, the measured length will converge to the true length.
Re: Is the average sinuosity of the world's rivers equal to pi?
#9What's the reasoning behind why this should be the case? Something to do with the curvature of the Earth?
Re: Is the average sinuosity of the world's rivers equal to pi?
#10Do rivers actually have a well-defined length? I know coastlines do not, and rivers seem similar. https://en.wikipedia.org/wiki/Coastline_paradox
Suppose you expanded every point of a coastline into a small disk (i.e. take the minkowski sum [1] of the coastline and a disk). Is the perimeter of the resulting shape still infinite?
The coastline had infinite perimeter because as you zoomed it got jankier and jankier. But once the janks get smaller than the disk, they start being hidden by disks from the surrounding points. You can't jump in and out anymore on tiny scales, because you run into the adjacent disks. This smooths out the noise and things converge instead of diverging.
... I think.
A river's length would smooth out for essentially the same reason. The set of points equidistant from both sides of the river is smoothed out compared to the sides because points on the side that are closer to the center of the river will hide jank from the nearby further points.
That's my intuition anyways. Not sure how it actually plays out.
Edit And if you go by "shortest path within the river from source to sink" as the length then it's definitely finite.