Photo by: Kathryn Schottl Figure 5: However, flower petals are not the only source of the Fibonacci sequence in nature. Seed heads are another place to spot the Fibonacci sequence in nature. Seed heads tend to form spirals just as with the petals this is for efficiency, the seeds grow from the middle pushing the other seeds out in a spiral pushing the oldest seeds out to the edge. This could go on indefinitely with new seeds constantly being produced and pushing out the older ones in a spiral formation. The spirals themselves are interesting, if you start counting the the sunflower seeds that are spiraling outwards in a clockwise direction in Figure 6 you should get 89 spirals at the edge in one direction and 55 spirals in the other direction at the edge again both numbers fall into the Fibonacci sequence. The same spiral sequence also appears in pine cones. If you look at Figure 7 and 8 you can see and count the spirals going in both directions. Figure 6:
Figure 7: Phyllotaxis is the arrangement of leaves on a team and in relation to one another [Mer]. Figure 8 shows how the leaves pattern of growth. The leaves grown in a pattern so that a leaf above doesn’t hide the leaf below so each leaf gets adequate sunshine and water. The starting leaf is marked with an X in figure 8. Notice how in Figure 8 the third and fifth leaf are both under the starting leaf. They are not centered under the starting leaf but some part of the leaf is under the starting leaf staring a new spiral. If you look closely you will see that the eighth leave is directly under the starting leaf. Notice that each leaf under the starting leaf is a Fibonacci number. The leaves under the starting leaf are not the only way you see the Fibonacci sequence in this particular plant. By looking down from the top of the same plant we looked at in Figure 8
we can see the Fibonacci sequence appear in spirals looking down from the top. There are five clockwise rotations passing 8 leaves there are also only 3 rotations in the anti-clockwise direction. The Fibonacci sequence appears in many places in nature. The spirals on the pine cone discussed also appear on pineapples, cauliflower, and even Romanesque Broccoli has beautiful spiral patters that also have numbers in the Fibonacci sequence. Figure 8: Figure 9:
Fibonacci and golden ratio in popular culture The Fibonacci sequence and the golden ratio have made their way into pop culture. The Fibonacci sequence has shown up in comic strips, television shows, books and movies. One popular book and movie that the Fibonacci sequence shows up in is the Da Vinci code by Dan Brown. In Robert Langdon uses the Fibonacci sequence to open a safe and the sequence is
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- Winter '15
- Andrew Martino
- The Da Vinci Code, Golden ratio, golden rectangle