January 2014 archive

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.


What is the relationship between the book “Nobody Knows” and the real world?

During G7 English class, I read my own book called “Nobody Knows”, which is written by Shelley Tanaka. Then, I found connections between my book and the real world. I had three connections between the book and the real world, and they are family, friends, and money.

My first connection is family. In the story, there is a one family that live in Tokyo. There are 5 members including Akira, Kyoko, Shige, Yuki and their mom. However, Yuki and Akira have different fathers. One day, their mom goes to Osaka to earn money. She promises to come back again soon, but she never comes back after she leaves them in Tokyo. Children are abandoned by their mom and they have no one to take care of them. Therefore, Akira has to look after his siblings. I learned that in the world, they are many poor abandoned children. Then, their family have to become “households headed by children”, and they will really hard to live without their parents. We have to understand the problem and find solutions to help them.


This is a picture of the family in Nobody Knows

My second connection is friends. For Akira, it was always difficult to make friends because other people used to bully him because he lives in a dirty house.  Later, he finally meets a  girl named Saki. Saki is a kind and friendly girl who helps them a lot. Saki gives money for them, and she plays with Akira’s siblings. I was moved by her braveness and I thought that we really need to help poor neighborhoods because some of the people in this world really need others’ help.


This is a picture of Saki and Akira in Nobody Knows

My last connection is  money. In this book, Akira, Shige, Yuki, and Kyoko do not go to school because their family cannot afford to send children to school. Also, their family is separated because their mom really needs to earn money in Osaka. Nowadays, the gap between the rich and poor is one of the big problem in the world.


This is a picture of the book

In the world, they are many people who suffer from the pressure of money. Also, there are many children who are abandoned by their parents and  have to take care of themselves. Some of them even have to look after their siblings. Some of the families need to be separated because they do not have enough money to maintain their living. This shows that the “Gap between the rich and poor” is one of the big problems. It will be great to help poor neighborhoods because even a little support can make them much happier. I realized that I need to thank people me for giving me happiness. Because of the great lesson that I learned from the book, I will never forgot this book.

Here is a video about an issue related to this book :