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Cracking Da Vinci’s Code On Tree Growth

Leonardo da Vinci certainly had an eye for detail – and a brain to match. Among his many musings was a theory that a tree’s branches grow in mathematical proportion to the diameter of its trunk. A French researcher now says he has the math to prove Da Vin

You do the math... (stephi2006)
You do the math... (stephi2006)
Sara Bovio

In winter, the sight of trees left bare after its leaves have fallen can leave some feeling gloomy. But for Renaissance genius Leonardo da Vinci, the view was a source of inspiration, which eventually led him to formulate a theory about the relationship between the size of a tree's truck and the combined measure of its branches.

Now, for the first time, a French researcher says he has come up with a scientific explanation for Da Vinci's 500-year-old theory.

In one of his more than 7,000 pages of notes, Da Vinci laid out his tree formula. He calculated that the squared diameter of a tree's trunk is equal to the squared sum of the diameters of its branches. Moreover, if a trunk is split into two sections, the sum of the thickness of all the branches coming off of one of the section is equal to the thickness of that section of trunk.

Up to now, no one had even offered scientific explanation to this theory. Christophe Eloy, a visiting professor at the University of California at San Diego and a specialist in fluid mechanics, may have finally found an answer.

Most botanists thought that the law of nature behind Da Vinci's formula was an efficient way to transport sap to leaves. Eloy disagrees. He thinks trees are structured as they are in order to protect themselves from damages caused by the wind.

Five years ago, Eloy became interested in Leonardo's formula and the mechanics of trees after reading the book Plaidoyer Pour L'arbre (Plea for the Tree) by Francis Hallé, a specialist in tropical forests. Eloy later attended a lecture by professor of fluid mechanics Emmanuel de Langre at the Ecole Polytechnique in Paris on the relation between wind and plants. "De Langre spoke about Leonardo's formula, and that it was like a Pythagoras theorem for trees, except that no one had explained it yet," he recalled.

A question of mechanical engineering

In his research, Eloy used an analytic model and a numeric model to computer-design the lightest possible tree structure that would still be able to resist the wind.

"In the first model, I developed some hypothesis to simplify the geometry of ramification. I took into consideration that a tree's shape is fractal by nature, meaning that the same pattern repeats itself in smaller structures, such as smaller branches," says Eloy. "The problem to explain is one of mechanical engineering, to understand how the diameter of the branches should change so that each point of the structure had same probability of breaking when the wind blows."

The numeric model was used in order to evaluate the effectiveness of some assumptions of the first model. "I used a simple scheme with few parameters to generate the skeleton of the trees in 3-D. Some of the copies of the principal branches were summed up repeatedly in order to create a virtual structure. The diameter of each branch was calculated against the constant of the probability of breaking in the wind," Eloy says. "The two models perfectly fit with each other and with Leonardo's formula."

This finding might have several applications, according to the researcher, including a better understanding of the mechanism of how plants grow and resist outside elements. It could be relevant for forestry and agricultural businesses, as well as bioengineering, says Eloy.

Such rules of nature occur every day under our eyes. But only Da Vinci, who as both a scientist and a painter, was an attentive enough observer of nature to be able to understand it.

"He analyzed and debated his discoveries in a very modern way," says Eloy. "His intuitions were clear and complex at the same time, and are studied and debated by scientists to this day."

Read the original article in Italian

Photo - stephi2006

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FOCUS: Israel-Palestine War

Palestinian Olive Trees Are Also Under Israeli Occupation — And That's Not A Joke

In the West Bank, a quieter form of oppression has been plaguing Palestinians for a long time. Their olive groves are surrounded by soldiers, and it's forbidden to harvest the olives – this economic and social violence has gotten far worse since Oct. 7.

A Palestinian woman holds olives in her hands

In a file photo, Um Ahmed, 74, collects olives in the village of Sarra on the southwest of the West Bank city of Nablus.

Mohammed Turabi/ZUMA
Francesca Mannocchi

HEBRON – It was after Friday prayers on October 13th of last year, and Zakaria al-Arda was walking along the road that crosses his property's hillside to return home – but he never made it.

A settler from Havat Ma'on — an outpost bordering Al-Tuwani that the United Nations International Law and Israeli law considers illegal — descended from the hill with his rifle in hand.

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After kicking al-Arda, who tried to defend himself, the settler shot him in the abdomen. The bullet pierced through his stomach, a few centimeters below the lungs. Since then, al-Arda has been in the hospital in intensive care. A video of those moments clearly shows that neither al-Arda nor the other worshippers leaving the mosque were carrying any weapons.

The victim's cousin, Hafez Hureini, still lives in the town of Al-Tuwani. He is a farmer, and their house on the slope of the town is surrounded by olive trees — and Israeli soldiers. On the pine tree at the edge of his property, settlers have planted an Israeli flag. Today, Hafez lives, like everyone else, as an occupied individual.

He cannot work in his greenhouse, cannot sow his fields, and cannot harvest the olives from his precious olive trees.

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