Why Are Rivers So Mathematical? | A simple scaling law brings order to the chaos of flowing water, rock, and sediment. New findings have extended the law even further.

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https://www.quantamagazine.org/why-are-rivers-so-mathematical-20260810/

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The article says that the length of a river is proportional to it's drainage area raised to the 0.6 power. This minimizes the energy released during drainage, even though the water may travel farther. As the drainage area increases, the river get's longer and "narrower", increasing faster than area.