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> ... Says nothing about his actual rule. Indeed! Here it is in brief from another article on the subject "...Leonardo’s rule [for how trees branch] says that

> ... Says nothing about his actual rule. Indeed! Here it is in brief from another article on the subject "...Leonardo’s rule [for how trees branch] says that the thickness of a limb before it branches into smaller ones is the same as the combined thickness of the limbs sprouting from it." https://www.sciencenews.org/article/leonardo-da-vinci-rule-tree-branch-wrong-limb-area-thickness https://www.sciencenews.org/article/leonardo-da-vinci-rule-t...

Retric 3y ago
That seems to again misrepresent the rule. He’s an artist drawing 2D objects not making 3D sculptures. The connection between the surface area of branches and overall tree structure shows that it’s the living, outer layers that guide tree structure, the researchers say. “The life of a tree flows according to the laws of conservation of area in two-dimensional space,” the authors write in their study, “as if the tree were a two-dimensional object.” Yes, a two-dimensional object like say a painting.
klyrs 3y ago
But now we know that most trees are living skin on a dead skeleton. If we assume a constant thickness of the vascular cambium, branches must conserve surface area, and not volume! Now, off to read the paper. Edit: aha, my proof is correct! Only, my axiom was wrong: trees make broader capillaries for thinner branches. Well played, trees.
- rob74 3y ago
  ...or, to quote the article: > Therefore, the plant has to reduce in its volume as it reaches its extremities, causing a higher ratio of capillary to the surrounding plant mass The way I read it: because branches at the extremities are thinner, the ratio of "living skin" to "dead skeleton" is higher. I'm just wondering why this isn't immediately obvious and why they are presenting this as a great discovery?! Also, the phrase "has to reduce in its volume as it reaches its extremities" sounds a bit backwards: sure, young branches are thinner, and as the tree grows and branches get older, they grow thicker to support the young branches that grow off them.
- Someone 3y ago
  > If we assume a constant thickness of the vascular cambium, branches must conserve surface area. Not necessarily. Transport speed could be different depending on the diameter of the branches Also, I would think a model that has a constant flow at each distance from the roots or the leaves is incorrect. A more realistic model has water being transported up and mostly evaporating in the leaves and barely contributing to tree mass, carbon (in some form) being transported down from the leaves and gradually being accumulated, and small amounts of minerals being transported up from the roots and gradually being accumulated. That model has a constant water flow throughout the tree, but a gradient in downward flow. I wouldn’t know which is dominant. _if_ most of the transport volume is carbon being transported down to branches and roots and being accumulated, more volume would go out of the leaves than arrives at ground level. I wouldn’t know whether that’s true, though. Most of a tree’s mass comes out of CO2 in the air, but because water evaporates out of the tree, there still may be more stuff going up than going down.

Retric 3y ago

That seems to again misrepresent the rule. He’s an artist drawing 2D objects not making 3D sculptures. The connection between the surface area of branches and overall tree structure shows that it’s the living, outer layers that guide tree structure, the researchers say. “The life of a tree flows according to the laws of conservation of area in two-dimensional space,” the authors write in their study, “as if the tree were a two-dimensional object.” Yes, a two-dimensional object like say a painting.

klyrs 3y ago

But now we know that most trees are living skin on a dead skeleton. If we assume a constant thickness of the vascular cambium, branches must conserve surface area, and not volume! Now, off to read the paper. Edit: aha, my proof is correct! Only, my axiom was wrong: trees make broader capillaries for thinner branches. Well played, trees.

rob74 3y ago
...or, to quote the article: > Therefore, the plant has to reduce in its volume as it reaches its extremities, causing a higher ratio of capillary to the surrounding plant mass The way I read it: because branches at the extremities are thinner, the ratio of "living skin" to "dead skeleton" is higher. I'm just wondering why this isn't immediately obvious and why they are presenting this as a great discovery?! Also, the phrase "has to reduce in its volume as it reaches its extremities" sounds a bit backwards: sure, young branches are thinner, and as the tree grows and branches get older, they grow thicker to support the young branches that grow off them.
Someone 3y ago
> If we assume a constant thickness of the vascular cambium, branches must conserve surface area. Not necessarily. Transport speed could be different depending on the diameter of the branches Also, I would think a model that has a constant flow at each distance from the roots or the leaves is incorrect. A more realistic model has water being transported up and mostly evaporating in the leaves and barely contributing to tree mass, carbon (in some form) being transported down from the leaves and gradually being accumulated, and small amounts of minerals being transported up from the roots and gradually being accumulated. That model has a constant water flow throughout the tree, but a gradient in downward flow. I wouldn’t know which is dominant. _if_ most of the transport volume is carbon being transported down to branches and roots and being accumulated, more volume would go out of the leaves than arrives at ground level. I wouldn’t know whether that’s true, though. Most of a tree’s mass comes out of CO2 in the air, but because water evaporates out of the tree, there still may be more stuff going up than going down.