# The Math Of Trees As Observed By Da Vinci and Fibonacci

I should sit around all day thinking of things which reporters will be impressed by that are common knowledge in science communities, so I can be famous with out having to do anything.

NPR is running a story about how a French scientist has proven that the surface area of trees are a result of the specific way they branch, helps them not fall over in hurricane winds.

"When a mother branch branches in two daughter branches, the diameters are such that the surface areas of the two daughter branches, when they sum up, is equal to the area of the mother branch."

Da Vinci and Fibonacci both documented this natural phenomena and it is the basis for the practical application of Fractal Geometry.

This is the Quintessential example from fractal mathematics. Knowing this relationship allows you to calculate the surface area of a Leafless tree, (or the bark Area) of a tree knowing only 3 things. The height, the diameter of the base, and the degree at which the tree narrows. (which is generally the same for all trees in a species)

For even more accuracy a coefficient can be chosen for the resolution at which you want to measure the surface area. the Surface area of most bark is not the same as the amount of wrapping paper that would cover it, because of the pits on the surface of the bark, but a fractal coefficient can be chosen for what measure you would use. When calculating wind resistance you might need a resolution that is at half a square Millimeter, but when you want to calculate how much bark you will get for your paper mill, you would only care at the resolution of the fore mentioned Wrapping Paper.