Fibonacci Furniture

The other day I was at my brother’s college and the carpet had a Fibonacci like pattern. I didn’t take a picture but this looks kinda close. 

So that made me think of other decor that may have the Fibonacci sequence. I found an article about an artist who created furniture based off of it.

It’s a table with several blocks of different sizes that you can arrange in different patterns and you can sit on it. It kind of shows how the Fibonacci sequence has multiple uses and that it’s not just one thing.

And here’s a picture of Homer.

The Golden Ratio and Pinecones

All week my kids and I have been finding super huge pinecones outside. I have been talking to them about the Fibonacci sequence in nature and the golden ratio. Hannah, my 13 year old spent some time counting the spirals and found 2 pinecones that didn’t exactly follow the Fibonacci sequence. We talked about mutation rates, etc. but also non-fibonacci sequences. We also spent some time looking for other spirals in nature. The kids found some cool plants and Matthew was convinced that the tree bark he saw showed the Fibonacci sequence, but I didn’t see what he saw. We spent some time at the site below and they all watched the Doodling in Math Class videos. Fun stuff!

 

http://jwilson.coe.uga.edu/emat6680/parveen/fib_nature.htm

 

History of the Golden Ratio

While looking around at Golden spirals and conspiracy theories, I found an interesting article on the History of the “Golden Ratio” and its origins. To me the most interesting part of math history is how long mathematicians have used some of these equation and theories and how many of them have endured the test of time

Many people think that the Pyramids and the Parthenon were designed with Phi in mind, but these conclusions are subject to debate. We do know for a fact that a couple thousand years ago, Phidias,Plato and Euclid had worked with Phi. They worked, just like us to apply the Golden Ratio to things in there time.

Leonardo Fibonacci born in 1175 discovered the Fibonacci sequence and its relation to Phi, which we discussed in class. Leonardo Da Vinci recognized the golden ratio or divine ratio as he referred to it. Da Vinci would use it in in work “The Last Supper”

Michael Maestlin was the first person to ever calculate the Golden ratio, his student Johannes Kepler the astronomer would also research the divine ratio. Some believe that Martin Ohm in 1815 was the first person to ever refer to the ratio as “golden” and it appears that name has stuck!

 

Here is the link to the article I read

https://www.goldennumber.net/golden-ratio-history/

Here is some further reading on Maestlin

https://en.wikipedia.org/wiki/Michael_Maestlin

 

Golden Ratio and the Human Face

I was searching online for different articles about the golden ratio and there were a lot of interesting ones online.  One that caught my eye was about the human face and how the golden ratio is even on our faces.  And the amount that they added up was incredible and not what I thought it would be.  This just goes to show yet again that math is everywhere.

https://www.goldennumber.net/beauty/

The Golden Ration in the Human Body

Everything that we have learned about the Golden Ratio has blown my mind, and this is no different. There are so many different ratios in our body that all ideally equal the Golden Ratio (1.618). This video gives a lot of examples, but the one that stood out the most was the one that took the height and length of the two front teeth.

I just found it so amazing that not only does it come up in plants and artwork, but the Golden Ratio can be found in our bodies as well.

The Silver Ratio

As we had discussed in class, the Golden Ratio is one that occurs in nature and has links to the Fibonacci Sequence. But it isn’t the only ratio in mathematics that can occur.

You can see if two quantities are in the Silver Ratio if the ratio of the smaller quantity and twice the larger quantity, is the same as the ratio of the larger one to the smaller quantity.

This is another case where we can spiral into rectangles over and over and over again using the same ratio. It correlates not with Fibonacci’s sequence but with another sequence of infinite numbers known as Pell’s Numbers. Here it is again in visual form:

As the spiral traces the progression of this ratio from both sides and not from only one (Which you can’t do with the Golden Ratio) you can see the pattern: Two squares of the exact same size and shape separated in the middle by another rectangle, which also has two squares separated by a rectangle, and so on. Another way to visualize the ratio is with a perfect octagon:

So, where in the real world would you go to look at something inspired by the Silver Ratio?

Japanese architecture up to the Edo Period often used the Silver Ratio as an inspiration for their buildings. The slanting rooftops are in the Silver Ratio with each other.

Musicality

If you’ve ever dabbled in music, you know that math plays a major role in music. So I did a little happy dance when I stumbled upon the Google search “Fibonacci Sequence Music.”

On a piano scale of C to C (one octave) there are 13 keys, consisting of 8 white keys and 5 black keys split into groups of 3 and 2.

Technically speaking there are only 12 notes in an octave, however the 13th note comes into play–and is necessary– when transitioning between octaves.

It’s “Time” for the Golden Ratio

As I was researching for more information on the golden ratio I found an interesting topic that was not discussed in class. The concept that the golden ratio has a correlation with space time and time in general and I thought this was really fascinating. Here are some websites with that speak more on the topic.

https://www.goldennumber.net/quantum-time/

http://www.sajs.co.za/system/tdf/publications/pdf/Boeyens_SciCo.pdf?file=1&type=node&id=34293&force=

I also found this really awesome documentary on math, the first part is about the Fibonacci sequence and then it goes into other forms of math and its relation to to universe but I thought it was really interesting and because I am such a huge fan of documentary’s I just had to share it.

Bees

I thought that the fact that the Fibonacci sequence showed up in how bee family tress go is pretty neat. It was also interesting to see that if you took the female or males and counted them that the sequence showed up in there too. I only figured this out because as I looked at the board I thought I recognized a pattern. Turns out it was the Fibonacci sequence.

The Golden Ratio in Real Life

Already knowing that the golden ratio can be found in virtually almost anything, I still did some googling. We already know that it’s found in nature in things like flowers, shells and pine cones, but it can also be found on a larger scale.

https://gnosticwarrior.com/wp-content/uploads/2015/07/hurricanes-galaxies-phi.jpg

Taking an earth science course last semester, I retained a bit of knowledge about storms such as hurricanes. The image on the left is an example of wind traveling long distances around Earth, which appears to be curving rather than moving straight across. This is know as the Coriolis Effect.

It is said that hurricanes and the golden ratio are connected because of the connection between the golden ratio and the spacing of spiral arms around a hurricane; the spiral arms never touch each other because they are all perfectly spaced apart in an orderly fashion. It is apparent that the golden ratio is at work here, and you can even see it when looking at a hurricane from bird’s eye view.