Romanesco Broccoli

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I decided to delete the other two lines and only keep the Fibonacci line and the line from the third set of broccoli ratios. I made a trend line for both and I displayed the equation. The y intercepts were different, however the slopes were nearly the same. They was only a 0.0116 difference between them.
I decided to delete the other two lines and only keep the Fibonacci line and the line from the third set of broccoli ratios. I made a trend line for both and I displayed the equation. The y intercepts were different, however the slopes were nearly the same. They was only a 0.0116 difference between them.
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The following is the graph:
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The following is the graph and proof the Romanesco Broccoli grows in accordance to the Fibonacci Sequence:
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[[image:Ratio_Graph.png]]
[[image:Ratio_Graph.png]]
|AuthorName=KatoAndLali
|AuthorName=KatoAndLali

Revision as of 16:44, 17 June 2013

Image:inprogress.png
Romanesco Broccoli
Field: Geometry
Image Created By: KatoAndLali
Website: [1]

Romanesco Broccoli

This is the Romanesco Broccoli, which is a natural vegetable that grows in accordance to the Fibonacci Sequence, is a fractal, and is three dimensional.


Contents

Basic Description

Although the broccoli looks like it grows in accordance to the Fibonacci sequence, does it really? By making ratios between the distances of the vertices of each iteration of the fractals, and then making ratios between the numbers in the fibonacci sequence, then plotting them, the growth of the broccoli in accordance to the sequence was proved.

A More Mathematical Explanation

Proof that the Romanesco Broccoli is a natural example of the Fibonacci sequence:

It looks as if the [...]

Proof that the Romanesco Broccoli is a natural example of the Fibonacci sequence:

It looks as if the Romanesco Broccoli is a natural example of the Fibonacci sequence. However appearances can deceive. A mathematical and scientific proof does not. I took the main image of the broccoli and I put points on each of the vertices of each fractal iteration. Then I connected each point and made line segments between them.

image:Ratios_Fibonacci_2.png


I then measured the line segments, and going from largest to smallest, I made ratios between the largest line segment and the next largest until the last line segment was reached.The image I used for this was a side view of the broccoli.

I repeated the process with an image of the broccoli from above.

image:Ratios_Fibonacci_1.png

I then took the first few numbers of the Fibonacci Sequence and created ratios between them from largest to smallest, just like I did with the line segments on the broccoli. I created a chart with all these ratios.

image:Table_of_Ratios.PNG

I took the chart and made a line graph with the ratios. I noticed that the line made by the ratios of the Fibonacci sequence was very similar to the line made by the third set of broccoli ratios.

image:Original_Ratio_Graph.PNG

I decided to delete the other two lines and only keep the Fibonacci line and the line from the third set of broccoli ratios. I made a trend line for both and I displayed the equation. The y intercepts were different, however the slopes were nearly the same. They was only a 0.0116 difference between them.

The following is the graph and proof the Romanesco Broccoli grows in accordance to the Fibonacci Sequence:

image:Ratio_Graph.png


Why It's Interesting

Interest


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