The golden ratio 1.618 is everywhere. It’s in old Iphone’s, buildings, plants and even Donald Trump

 

 

 

 

The golden ratio has also been found in many ancient art pieces because it is astecticly pleasing and is often used in spirals and rectangles. You can see the golden ratio multiple times in:

Da Vinci’s “Last Supper”

And Giovanni Bellini’s “Madonna in the Meadow”

We learned about numbers, exponents, and radicals in this unit. The golden ratio is equal to 1.6180339887… This is a Irrational number because the digits keep going on without a pattern. It is believed that the golden ratio is the most irrational number.

Earlier in the year we also learned about trigonometry and I figured out that the Golden Ratio is also equal to 2 × sin(54°)

For this project I decided to focus on the golden ratio in art because I love to draw whenever there’s a chance in projects. I decided to draw a snowy scenery because Christmas is coming up and when we started this project it was starting to get snowy on the mountain.

the fist thing I did was come up with ways to show the golden ratio in a snowy scenery. I found out that you can demonstrate the Fibonacci sequence in a tree.

 

As you can see, the number of branches in each row add up to the pattern of the Fibonacci sequence. But how does the golden ratio relate to the Fibonacci sequence you might ask.

The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

When you divide each number by the previous number This is what you get:

1, 2, 1.5, 1.666…, 1.6, 1.625, 1.615…, 1.619…, 1.6176…, 1.6181…, 1.6179…

as you can see it gets very close to the golden ratio

I also decided to use the golden ratio 1.6 to 1, in a circle. I first was going to have a moon and a sun but later decided to have the ratio in the moon and the shadow

Lastly I placed my tree and moon accordingly to the Golden ratio spiral