How does fibonacci sequence relate to nature

Seeds in a sunflower head. The number of spirals pointed left and right are consecutive numbers in the Fibonacci sequence. Photo Credits : Pixabay. Photo Credits: Pixabay How strange is that? An Evolutionary Perspective Nature is not an entity that consciously follows mathematics flowers are not the smartest.

Post Views: 11, Eman Toosy Member since Previous story : The Dance that Spins Spacetime. More from Eman Toosy. The Key to Immortality: Jellyfish. Deep in the vast abyss of the ocean, roams a creature that might hold the elixir to immortality. When this creature of wonder dies, it rises again from its own remains… Humans, throughout history, have embroiled themselves in the quest for immortality. Beginning from early pursuits into alchemy to modern-day anti-aging means, the eagerness to […].

Written by Eman Toosy Saving Bookmark this article Bookmarked. The Queen of Science, Mary Somerville. Up until the late 19th and 20th centuries, people — mostly men — connected with science were referred to […]. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns. In some cases, the seed heads are so tightly packed that total number can get quite high — as many as or more.

And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling namely one that will not be well represented by a fraction. Phi fits the bill rather nicely. Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers.

For example, a cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right. Likewise, similar spiraling patterns can be found on pineapples and cauliflower. The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant.

This pattern of branching is repeated for each of the new stems. A good example is the sneezewort. Root systems and even algae exhibit this pattern. The unique properties of the Golden Rectangle provides another example.

It's call the logarithmic spiral, and it abounds in nature. Snail shells and nautilus shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider's webs. Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern.

The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees. As an interesting aside, spiral galaxies appear to defy Newtonian physics.

As early as , astronomers realized that, since the angular speed of rotation of the galactic disk varies with distance from the center, the radial arms should become curved as galaxies rotate. Subsequently, after a few rotations, spiral arms should start to wind around a galaxy. But they don't — hence the so-called winding problem. The stars on the outside, it would seem, move at a velocity higher than expected — a unique trait of the cosmos that helps preserve its shape.

Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself which follows along a spiral.

It's worth noting that every person's body is different, but that averages across populations tend towards phi. It has also been said that the more closely our proportions adhere to phi, the more "attractive" those traits are perceived.

As an example, the most "beautiful" smiles are those in which central incisors are 1. It's quite possible that, from an evo-psych perspective, that we are primed to like physical forms that adhere to the golden ratio — a potential indicator of reproductive fitness and health. Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the ratio of phi.

Even our bodies exhibit proportions that are consistent with Fibonacci numbers. For example, the measurement from the navel to the floor and the top of the head to the navel is the golden ratio.

Animal bodies exhibit similar tendencies, including dolphins the eye, fins and tail all fall at Golden Sections , starfish, sand dollars, sea urchins, ants, and honey bees. Speaking of honey bees, they follow Fibonacci in other interesting ways. The most profound example is by dividing the number of females in a colony by the number of males females always outnumber males. The answer is typically something very close to 1. In addition, the family tree of honey bees also follows the familiar pattern.

Males have one parent a female , whereas females have two a female and male. Thus, when it comes to the family tree, males have 2, 3, 5, and 8 grandparents, great-grandparents, gr-gr-grandparents, and gr-gr-gr-grandparents respectively. Following the same pattern, females have 2, 3, 5, 8, 13, and so on.

And as noted, bee physiology also follows along the Golden Curve rather nicely. When a hawk approaches its prey, its sharpest view is at an angle to their direction of flight — an angle that's the same as the spiral's pitch. Even the microscopic realm is not immune to Fibonacci.

The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1. Get Directions. Math Enrichment and Accelerated Programs in Pflugerville. Did you know Mathnasium offers enrichment programs for students? Mathnasium is where students in Math Success in the Spring Semester. The Spring Semester is underway and classrooms are gearing up Toggle navigation.

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Arrangement of leaves on a stem. Another simple example in which it is possible to find the Fibonacci sequence in nature is given by the number of petals of flowers. Sources: Tesi di Laurea in biomatematica: La successione di Fibonacci nella fillotassi — Laura Resta Le geometrie delle piante e la successione di Fibonacci — Scientificast.

Energy and environment. The numbers of nature: the Fibonacci sequence The Fibonacci Sequence has always attracted the attention of people since, as well as having special mathematical properties, other numbers so ubiquitous as those of Fibonacci do not exist anywhere else in mathematics: they appear in geometry, algebra, number theory, in many other fields of mathematics and even in nature!

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You can see how each set of leaves spiral outward. The Fibonacci spiral is a little more subtle in this photo, but you can still see the spiral in the unopened disk florets.

Marlborough Rock Daisy by Sid Mosdell. Again, the spiral is visible in the disk florets of the flower. All pinecones display a Fibonacci sequence. The umbo on pinecones increases in size as you move outward, displaying a Fibonacci spiral. The Pangolin is able to protect its soft underbelly by forming a Fibonacci spiral.

This flower exhibits two Fibonacci spirals. You can faintly see how the spirals form from the center of the opened disk florets. Fibonacci in spores. A fiddlehead or koru. Snails and fingerprints. Both have a distinct Fibonacci spiral. Water falls into the shape of a Fibonacci sequence during numerous events.

Another example would be a vortex. One blogger has applied the Fibonacci sequence to population density and land mass.

In Africa the majority of highly populated cities fall on or close to where the spiral predicts. A Shell Fossil with the Fibonacci sequence. You can see as the shell grew, a Fibonacci spiral was formed. The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci.