Golden Ratio

Math is everywhere and it effects the way we view things. Math is in architecture, nature, and even on you. In this unit in math we learned about the golden ratio and how it makes things more aesthetically appealing. The golden ratio is a ratio of 1:1.618… and it is more appealing to the human eye. We also learned about the golden spiral which is a spiral within a rectangle with the golden ratio. 1.1618… is considered to be the perfect number and that is why shapes and items are more visually appealing when they have that number somewhere in their measurements.

The golden ration and spiral are found in many famous art pieces such as the Mona Lisa and is also found in nature in hurricanes.

For this unit our project was to make a piece of art using the golden ratio. The art could be anything from a drawing or a sculpture, to a song. We had to make this piece of art authentic and original. I decided to draw a picture because I love to draw. It took me a while to decide what to draw because I wasn’t sure if I wanted to do a nature scene or a single item. I ended up deciding to do a nature scene and I chose to draw a beach because I find them very beautiful and I wanted to find out how much the golden ration could possibly be at beach. I also wanted to make it a little abstract to make it more creative.

To start off I looked at pictures of the beach to find different ways I could incorporate the golden ratio. Here is one of the pictures that helped inspire me.

It inspired me to draw a wave using the golden spiral. I also liked the trees in the background and I wanted to incorporate more nature into my drawing so I decided to add a tree. I wanted to play with the depth in my picture so instead of having a tree next to the wave, I decided to put a branch in front of the wave. My plan originally was to have one shape in each section of the scene and use the golden ration in those shapes. I started off by filling the sky with rectangles, I then started to fill the beach with triangles and the ocean with circles but the measurements weren’t working out the way I planned so I had to scrap the beach and ocean shapes. Once I had completed the drawing I got to colour it in. I didn’t want the sky and the ocean to both be blue so I decided to do a sunset in the sky so I could add more colours. I also added a line outlining the sun that I later removed because it was unnecessary. Once my picture was complete it was time to label the measurements.

For the measurements we had to label some of the golden ratios with decimals and some with radical notation. Here is an example of how to label a rectangle with radical notation.

I measured and labeled all of my golden ratio rectangles and golden spirals. I measured about half with decimals and half with radical notation. I also drew the leaves to have their diameters be to the ratio of 1:1.618… in each pair of leaves. None of the shapes have the lengths of 1:1.618 but they have that same ratio. On each rectangle the width is the length times 1.618. Once all of the labeling was complete I was ready to hand in my project.

I really enjoyed this project. It was a very fun way to use math in art. I loved the freedom of this project because it allowed me to be creative and do something I liked. I am really proud of how my project turned out and I hope we do more projects similar to this in the future.