Careful examination of the patterns of alternate leaves shows them spiraling around the stem. This pattern can be expressed as a fraction. The numerator – the upper number of the fraction – indicates the number of spirals needed to complete the pattern while the denominator – the lower number of the fraction – the number of leaves or branches needed to complete the spiral. While the numbers in the fraction are frequently Fibonacci numbers, they may also be alternate numbers so that instead of say 2/3 it could be 2/5 where the intervening number is a “3.”

Thus elm tree leaves have a pattern of ½ while the pear tree leaves have 3/8. Each species has its own specific phyllotaxis.

Everyday Fibonacci Spirals – Parastichy

Parastichy is defined as secondary spirals winding in opposite directions in certain botanical structures. Huh?

Fresh pineapple appears on many tables. The spirals literally stare us in the face.

The spirals literally stare us in the face.

The segments that characterize the peel form spirals. In fact, if you check carefully in the graphic example shown, you will find three sets of spirals each with a Fibonacci number. In one direction there are 5 spirals, in the other direction there are 8 spirals and vertically, off-center there are 13 segments.

Pine trees abound scattering their cones. These cones are mainly of interest as decorations at holiday times -Thanksgiving or Christmas . Looking carefully, the spiral patterns are obvious. In the clockwise direction there are 8 spirals and 13 in the counterclockwise direction. Further from the stem there is another series of clockwise spirals that number 21.

The last example I will share is the lovely sunflower. In this case and in many other flowers from the Asteraceae family, the florets growing from the center of the flower form spirals. Here you can see 21 spirals curving to the right and 34 spirals curling to the left.

Pretty soon you will be seeing spirals everywhere!

First looking at trees, we will now examine the branching structure of secondary branches growing off the trunk. “Some plants express the Fibonacci sequence in their growth points, the places where tree branches form or split. One trunk grows until it produces a branch, resulting in two growth points. The main trunk then produces another branch, resulting in three growth points. Then the trunk and the first branch produce two more growth points, bringing the total to five.”

By drawing straight lines through the branching points, the pattern can be easily seen.

Other plants such as the Sneezewort exhibit similar Fibonacci growth patterns.

I hope to wrap up this topic with my last installment.

If you are enjoying this topic, please consider purchasing my book A Habit of Seeing: Journeys in Natural Science.

Quite interesting how things happen in nature. And the importance of rabbits to number theory. Thank you for helping us see things in different ways.

Michael Conley

Fascinating. Thanks for sharing!

Esther Lewittes

Thank you so much. You help us to see the world in new ways. You offer so much . I recommend to everyone , to purchase your book. It is indeed a new world, that you offer us.

Kate RussellThat was fascinating! I always knew plants were interesting, but you’ve shown me how to take it to an entirely new level!

luis fonsecaQuite interesting how things happen in nature. And the importance of rabbits to number theory. Thank you for helping us see things in different ways.

Michael ConleyFascinating. Thanks for sharing!

Esther LewittesThank you so much. You help us to see the world in new ways. You offer so much . I recommend to everyone , to purchase your book. It is indeed a new world, that you offer us.