The first example is flowers. There are two basic ways that a flower will grow: flowers will either always have the exact same number of petals as other flowers in their species, or they will have a random number. As far as the first type of flower is concerned, many of those flowers with exact numbers of petals have a Fibonacci number of petals. In the other type, the average number of petals is often a Fibonacci number.

     Fibonacci numbers also appear in pinecones. If you look at the bottom of one, you can see swirls. If you count the number of little scales in one swirl, it'll be a Fibonacci number. The same pattern is found in the center of sunflowers.

      These are all arithmetic principles, because they have to do with counting. Appearances in structure are considered geometric, and there are several of those as well.

Geometric principles in botany...