Michael Gilleland of Laudator Temporis Acti quotes Leonardo da Vinci on the mathematics of trees:
All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk [below them]. . . .
Every year when the boughs of a plant [or tree] have made an end of maturing their growth, they will have made, when put together, a thickness equal to that of the main stem; and at every stage of its ramification you will find the thickness of the said main stem; as: i k, g h, e f, c d, a b, will always be equal to each other; unless the tree is pollardif so the rule does not hold good.
As Gilleland points out in his fascinating and meticulously documented article, recent studies show that Leonardo was pretty close to the mark. According to Tyree and Zimmerman (2002):
Although there is no evidence that Leonardo ever did any measurements to confirm this remarkable observation, botanists are well aware of the approximate correctness of this statement; measurements were made around 1900 to investigate the significance of stem dimensions in satisfying both mechanical and hydraulic demands....
Now here's your extra credit question: How can you tell the drawing above is by da Vinci?