Abstract - About 1500, Leonardo da Vinci sketched a tree with arcs through each yearly growth of branches. In his mirror-image handwriting, and including an equation, he noted that the sum of the thicknesses of all the new branches produced each year will equal the sum the thicknesses of branches from each previous year, down to and including the trunk. He wrote further that the same relation exists between a main watercourse and its branches. Leonardo's tree and notes clearly ilustrate the principle of stream ordering in drainage-network composition. Indeed, Leonardo combined network morphometry and hydraulic geometry, which together have thus far been inadequately investigated. Leonardo's tree drawing marks the discovery of quantitative drainage-network analysis, which was rediscovered by R.E. Horton more than four hundred years later. We use it to combine science and art in K-12 education.
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