The Fibonacci Sequence, Golden Ratio, Same Thing?

Honestly, I really enjoyed this project. It gave me the chance to dive deeper into something I’ve been fascinated by for the past few years. Not only because it’s the most aestchically pleasing ratio in the galaxy, but how it seems to be around every corner, responsible for everything in nature, and is why the universe is designed the way we know it today. The project for this unit was to create an art piece. Not just any creation, but one that includes as any golden ratios as possible. I used to be extremely into visual arts but with y increasingly busy schedule I’ve been slacking off. So this gave me the chance to relive my old passion. You know the words, Fibonacci Sequence and Golden Ratio, now let me tell you a little bit more about them.

The name Golden Ratio or Golden Number , named “phi” by the Greeks for the Greek sculptor Phidias. However, this ratio can be found in art and architecture long before the Greeks. The Great Pyramid of Giza built around 2560 BC is one of the earliest examples of the use of this ratio. The length of each side of the base is 756 feet, and the height when built was 481 feet. 756/481=1.571725572. The Parthenon in Athens, Greece, built in 440BC, exemplifies the use of the golden rectangle in many of the dimensions. The space between the columns, height to width, are in proportion to the golden ratio. As are most of the other exterior dimensions. However, it was hidden for

Phi, 1:1.61803398875…
Phi is technically the twenty-first letter of the Greek Alphabet, but it is more commonly known simply as the symbol for the Golden Ratio. 1 to 1.61803398875.. continuing on forever, it is an irrational number. Non-terminating yet it is considered to be the most aesthetically pleasing ratio for art, architecture and including in nature. It appears in things such as waves, the pattern of flower petals, as well as the rings inside of trees. It’s been used for centuries in art, first hidden by the church and held solely for use by artists. The most famous work that includes it is the Mona Lisa by Leonardo DaVinci. However, at the time he didn’t know about this perfect ratio, yet he was able to bring everything to be perfectly symmetrical, which is why it’s so pleasant to look at. Once studies using Phi had begun they discovered that this art piece fits perfectly into the ratios, proving how satisfying this ratio really is.

Fibonacci Sequence
1, 1, 2, 3, 5, 8, 13, 21… Adding together the two previous numbers, this is the Fibonacci Sequence. This natural phenomenon appears every where, in art pieces once again, nature, and stretching as far as our universe. Not only are things such as our Milky Way galaxy following the shape of the perfect spiral, but the shape of the entire universe is presumed to fit it as well. The findings from the 2003 NASA Wilkinson Microwave Anisotropy Probe on cosmic background radiation reveal that the universe is finite and is in fact shaped like a dodecahedron. A geometric shape that is based entirely on pentagons, which are based on Phi and the Sequence. This sequence relates directly back to the Golden Number. The ratio of each successive pair of numbers in the sequences approximates Phi (1.618..), as five divided by three is 1.666, and eight divided by five is 1.6.

My Project
For my project I really wanted to focus on the aesthetics of these supernatural numbers. Taking the Fibonacci Sequence as well as the perfect spiral and turning them in to an art piece. I started by sketching some ideas how to lay everything out and settled on working with the perfect rectangle. A series of Fibonacci squares that are in perfect ratio as well. Starting with the smallest squares, which were two side by side, 1x1cm squares. Then to the next number in the series, a 2×2 square. Then to 5x5cm, 8x8cm, 13x13cm, 21x21cm, and finishing with 34x34cm. These numbers are all a part of the Fibonacci Sequence, therefore fitting into the golden ratio of 1.618 as well. To show some more understanding of the lessons I decided it would also be beneficial to layer a slight, but noticeable spiral on top of these calculated squares. In order to do this I could have simply taken the glue and roughly drawn the radiuses of each square according to where the side of the rectangles were but decided it’d be best to calculate them. So I managed to find all of the radiuses for each square, then drew them out onto paper. Placing these pieces of paper down onto the canvas allowed me to form an exact spiral that worked according to the Fibonacci Sequence and the Golden Number of Phi.

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    • Kate Rogers

      Hi Simon,
      I have zero issues regarding your use of the photo and the art created; please let me know where I can see it featured!

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