Archive of ‘Mathematics’ category

Math – Box and whisker diagrams

During the math class, we worked on “Box and whisker diagrams”. The task that we needed to do was choosing two cities and comparing temperatures. For the cities, I chose Tokyo and Sydney. I chose January, June, and December for the months and I worked in fahrenheit.

These are the screenshot of Tokyo and Sydney :

Screen Shot 2014-05-29 at 8.51.13 PM

Screen Shot 2014-05-29 at 12.38.42 PMFor the January, Sydney’s min was 31.8 fahrenheit higher than Tokyo’s min, which is 65.6-33.8=31.8. Also, Sydney’s max was 31 fahrenheit higher than the Tokyo’s max, which is 66.9-35.9=31. Secondly, their medians were different, which is the middle date of the month(16). Sydney’s median was 32.3 fahrenheit higher, which is 66.4-34.1 = 32.3.

For the June, also Sydney’s min was 11.9 fahrenheit higher than Tokyo’s min, which is 47.8-35.9 = 11.9. However, Sydney’s max was lower than Tokyo because Sydney’s max is 51, and Tokyo’s max is 68.9. Therefore, I can know that Tokyo’s max is 17.9 fahrenheit higher than Sydney (68.9-51 = 17.9). Secondly for the medians, Tokyo’s median was higher than Sydney, which is 65.6-49.25 = 16.35

Lastly, for the december, Sydney’s min was 28.2 fahrenheit higher than Tokyo, which is 62.7-34.5 = 28.2. Also for max, Sydney was 23.6 fahrenheit higher than Tokyo, which is 66.6-43 = 23.6. For the medians, also Sydney was 26.15 fahrenheit higher than Tokyo, which is 64.7-38.55 = 26.15.

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

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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

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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

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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.

 

Pythagorean Theorem

Topic : What conclusions can you now come to about the Pythagorean theorem?

1. polygons

2. rectangle

3. square

I think pythagorean theorem works only for regular polygons (same sides) sharing the sides of a triangle. When the sides of a polygon are the same, the bigger area equals to the sum of the two smaller polygons. For example, this is because if we calculate the area of a square, it will be s² (when the length of a side equals to s). Therefore, the side of the triangle should be √(the area of a square).

On the other hand, other polygons, like a rectangle, they usually have different length and width. Therefore, two smaller areas plus the bigger area do not equal.


Marine Tower

During the math class, we went to the Marine tower for the field trip. First,before we arrive at the top of the marine tower, we made several guesses to estimate the distance between marine tower and other landmarks. Then, we went to the top of the Marine Tower. Marine tower is built on 15th of January, 1961 and it is 106 meters tall. In Marine tower, we could get a lot of information.

Here are some information about Landmarks:

1. Mount Fuji : 84km

2. Motomachi Arch : 300m

3. Toyko Skytree : 3.2km

4. Yokohama Stadium : 900m

5. Kaze-no Tower : 17.5m

6. Foreign cemetery : 500m

7. Osanbashi terminal : 500m

8. Yokohama Baybridge : 2.4km

9. Minatomirai : 2km

10. Hommoku mart : 3km

11. Twiny Yokohama : 4.5km

12. Sea paradice : 1.2km