Leonardo's Rule of Trees Was Elegant—and Wrong

Branching Beyond Leonardo: The Evolution of Tree Architecture Theory

Leonardo da Vinci's rule of trees—that the total cross-sectional area of branches at any height equals that of the trunk—has guided artists and botanists for five centuries. Modern research has chipped away at it: a 2022 Physical Review E study found that what's conserved is two-dimensional projected area, not cross-section; a 2023 PNAS paper showed xylem conduits must widen toward branch tips for efficient water transport. The rule even shapes how we recognize trees in art.