The Golden Ratio

During the math class, we learned about the golden ratio.  Then, we researched about the relationship between the golden ratio and art, architecture, and music. Golden ratio is  1 : 1.168, which is also known as Phi.

1. Art


The picture of Mona Lisa

Leonardo Davinci was one of the artists who used the golden ratio. If we look at the picture of Mona Lisa, the woman’s face (width and length) equals to the golden ratio. “Mona Lisa” includes lots of golden rectangles. If we draw golden squares inside the golden rectangle, we can discover that the edges of squares are all on the important focal points of the woman, such as her chin, her eye, her nose, and the upturned corner of her mysterious mouth. It was believed that Leonardo Davinci tried to apply mathematics into art.

2. architecture


The picture of The Great Pyramid of Giza

The Great Pyramid of Giza is a one of the examples that showing the existence of golden ratio in architecture. If we pretend there is a right triangle within the pyramid, the base of the right triangle above equals to 1 and the height equals to √1.618. Then, the hypotenuse of the right triangle will be 1.618. Therefore, we can say that the great pyramid of Giza is made out of golden ratio.

3. Music


The picture of music

Fibonacci and phi(1.618) relationships are usually found in the timing of musical compositions. For example, the climax of songs is often found roughly around the phi point (61.8%) of the song, as opposed to the middle or end of the song.  For example, in a 32 bar song, the climax would occur in the 20th bar.


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