Significance and Application of the Fibonacci Sequence

For an introduction into the applications of Fibonacci sequences, listen to this podcast:



Podcast Script

Fibonacci Numbers in Nature

The ratio of a Fibonacci number divided by the next consecutive Fibonacci number approaches 0.618 (also the inverse of the Golden Ratio). This ratio is used by plants like sunflowers to help them effectively pack as many seeds in as they can. A sunflower is an example of one of these plants. As each seed is placed in its spot in the flower, it will be rotated 0.618 times. This is equivalent to 137.5 degrees (Pierce, 2017).
You can explore this angle-and try some other ones in the Geogebra Applet below.


(Pearcy, 2013)

Fibonacci numbers are also in the number of spirals in sunflowers and other plants like pinecones. Vihart's video below has many great example of such spirals:

Fibonacci Retracement

Not only are the Fibonacci numbers in nature and art, but it is also used in data and computer programming. They can also be useful for investing.

In the stock market, a stock moves in a general direction. Stocks tend to stop at the Fibonacci ratios mentioned in the podcast before continuing their trend. This process is called Fibonacci Retracement and can be used by investors to help them predict the stock market. The graph below shows an example of this:

(Cheekong, 2012)

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