Fibonacci Numbers in Nature: One of the most common places to see Fibonacci numbers is in the growth patterns of plants. Growth spirals are characterized by both a circular motion, and elongation. As a branch grows, it produces leaves at regular intervals, but not after each complete circle of its spiral. The reason the leaves are not directly above each other is because all of the leaves would not be able to get the necessary elements. It appears that leaves are generated on the stem in phyllotactic ratios where the numerator and denominator are both Fibonacci numbers. The numerator is the number of turns, and the denominator is the number of leaves past until there is a leaf directly above the original. The number of leaves past, ad both directions of turns produce 3 consecutive Fibonacci numbers. For example, in the top plant on this transparency, there are 3 clockwise rotations before there is a leaf directly above the first leaf, passing 5 leaves along the way. Notice that 2, 3, and 5 are all consecutive Fibonacci numbers. The same is true for the bottom plant, except that it rakes 5 rotations for 8 leaves. We would write this as 3/5 clockwise rotations per leaf on the top one and 5/8 for the bottom. Although, these are just computer-generated plants, the same is true in real life. A few real life examples of these phyllotactic ratios are 2/3 elm, 1/3 black berry, 2/5 apple, 3/8 weeping willow, and 5/13 *censored* willow. Daisies display Fibonacci numbers in their own unique way. If we look at this enlarged seed head of a daisy, and took the time to count the number of seeds spiraling in clockwise and counter clockwise rotations we would arrive at 34 and 55. Note that these are consecutive Fibonacci numbers. Many other flowers exhibit Fibonacci numbers not only in their buds and seeds, but also in the count of their petals. Most daisies have 13, 21, or 34 petals. Other examples would be as follows 3 – lilies, 5 –wild...
