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Mathematics

What da Vinci saw in trees

In his notebooks (pictured), the fifteenth-century Italian polymath Leonardo da Vinci observed that the total cross-section of a tree remains the same along its height every time it branches. Physicists have searched for years for an explanation for this phenomenon, but have yet to find one that is widely accepted.

Credit: T. LE MAGE/RMN (INST. FRANCE)

Christophe Eloy of Aix-Marseilles University in France shows that the observation follows from two assumptions — first, that trees are fractal, or self-similar in nature, and, second, that their growth is determined by the need to withstand wind stress on their branches. Eloy says that the most relevant property of wind loads is the way it diverges towards the tips of branches. Static loads from fruit, snow or ice would have a similar effect.

Phys. Rev. Lett. 107, 258101 (2011)

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What da Vinci saw in trees. Nature 480, 417 (2011). https://doi.org/10.1038/480417a

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