The Golden Ratio

Chapter 3 Project

Chapter 3 Math Project

For chapter 3, I chose the project The Golden Ratio. For this project, we had to draw or paint a scene in which the Golden Ratio was in it three or more times. First I will explain a bit more about the Golden Ratio.

About Phi (Φ), the Golden Ratio

Phi (uppercase Φ, lowercase φ, or math symbol ϕ), is the 21st letter of the Greek alphabet. No one exactly knows who invented and used phi, but we do know that phi appears in the Greek Pantheon building, but it is unsure if it was meant to be that way. Some people think some Egyptians might have used it in the Great Pyramids. Phi has been used in a lot of art and architecture.

The Golden Ratio, the Beautifully Irrational Number

The Golden Ratio has been used a lot on art and architecture. Some people say that the Golden Ratio makes the most pleasing rectangle shape. Think of the Mona Lisa - and the Golden Ratio, which might be another cause of the painting being so impressive.

The actual Golden Ratio is 1.61803398874989484820..., but we often round it to 1.6

In the Golden Ratio, the rule a+b is to a as a is to b means that the longer part divided by the smaller part also equals to the whole length divided by the longer part.

The Golden Ratio in a Simple Aquarium

Big image
In the above picture and the five pictures below I have incorporated the Golden Ratio. I have used the Ratio 6 times - once for a boat, once for a small castle, twice for two different fish, once for the smaller fish's eye, and finally once for the frame of my drawing. I checked all my measurements so that they all equal 1.6

Above, for the frame, my length is 25.7 cm's and the width is 15.8 . And 25.7 / 15.8 = 1.6


From this ratio, 1.61803398874989484820..., 1.6 , I learnt how this ratio is simply just a number without a pattern of decimals but makes the most pleasant rectangle, and how for that reason so many artists and architects have used it. I learned how to actually make the original Golden-Ratio-rectangle larger; this is done by multiplying 1 by any other number, and then multiplying 1.6 by the same exact thing.

I can prove this: take the number 8 for instance. 1 * 8 is obviously 8 - now I multiply 1.6 * 8, the same thing, and I get 12.8 . So to see if it's really the Golden Ratio I simply do the operation 12.8 divided by 8 = 1.6 - I got the Golden Ratio.