{
  "id": 476170,
  "title": "Why Are Rivers So Mathematical?",
  "url": "https://urgent.news/2026/08/10/why-are-rivers-so-mathematical",
  "topic": "science",
  "section": "Science",
  "published": "2026-08-10T14:56:34.000Z",
  "source": {
    "name": "Quanta Magazine",
    "slug": "quanta-magazine",
    "url": "https://www.quantamagazine.org/why-are-rivers-so-mathematical-20260810/"
  },
  "original_language": "en",
  "account": "Rivers have captivated humanity for centuries, from the London Thames to the Texas Blanco. These winding waterways share a common thread: they all follow the same mathematical rule. University of Minnesota river scientist Chris Paola marvels at the patterns of branching networks found in rivers, trees, veins, train lines and highways. Geomorphologists have long studied the geometry of river systems, dating back to the late 1800s. In 1957, USGS scientist John Hack discovered Hack’s law, which states that a river’s length is always proportional to its drainage area raised to the power of 0.6. This power law appears consistent worldwide, from small streams to mighty rivers. The reason behind this seemingly universal constant has puzzled scientists for decades. The law contradicts the expectation that stream length would follow a different power law, like the square root of the drainage area. This discrepancy suggests that river networks are more energy-efficient when they elongate at larger scales, leading to a directional flow toward the ocean. While the exact mechanism remains a mystery, Hack’s law has provided invaluable insights into the mathematical nature of river systems.",
  "summary": "A simple scaling law brings order to the chaos of flowing water, rock, and sediment. New findings have extended the law even further. The post Why Are Rivers So Mathematical? first appeared on Quanta Magazine",
  "key_points": [
    "Rivers follow mathematical rule of branching networks.",
    "Hack’s law states river length proportional to drainage area^0.6.",
    "Law suggests energy-efficient elongation of river networks."
  ],
  "editors_take": null,
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}