Sunday, April 10, 2016

Mathematics in Art

In this week's lecture, Professor Vesna talked about different mathematical concepts used in art, mostly paintings, like the linear perspective, vanishing points, and golden ratio. When the painters started to using these mathematical techniques in their works, the paintings became more realistic. In linear perspectives, parallel lines that receded into the distance appear to be converging together. And when artists want to recreate a three dimensional object, like a building for example, onto a two dimensional surface, they can use the linear perspective to give the audience a more realistic view of the scene. A lot of the Western paintings of buildings, space, and human body utilized linear perspectives.


Perspective diagram of Masaccio's Holy Trinity

And mathematics were not just used in art paintings, but also in architecture as well. Some people say that the Egyptian pyramids were built according to the golden ratio. If you use half of the baseline length of the pyramid divided by the slope length, you will get 1.168, which is the perfect golden ratio. However, whether the relation to golden ratio is by design or by accidents still remains a question


Ancient Greeks used the golden ratio when building the Parthenon.


Modern application of mathematics in architecture

I would like to introduce something different from most examples of math in art, which are mostly Western art. In fact, Chinese paintings often used complex mathematical techniques as well. The most famous one would be Along the River During the Qingming Festival, a long scroll painting that captured the daily life of the people and the landscape in the Capital from the Northern Song period.


Displayed in the painting is a water mill. This is only a very very tiny portion of the long scroll painting, because the whole painting is impossible to be embedded here.

Different from Western paintings where the painters usually use only one viewpoint and one vanishing point, Chinese paintings usually use several vanishing points. This is called scattered perspective. The painters' perspectives are moving when they observe the objects, so they can better exhibit all aspects of objects has large span in space.

I think the application of mathematics in paintings allowed the artists to create more accurate, realistic, aesthetic dictions of scenes. It has always been a great component of art.

Citations:

 "Architectural Icons Inspired by Mathematics." Whitesp Ce. 2013. Web. 11 Apr. 2016. <https://whitespacebkk.wordpress.com/2013/02/11/architectural-icons-inspired-by-mathematics/>.

Mize, Dianne. "A Guide to the Golden Ratio (AKA Golden Section or Golden Mean) for Artists." A Guide to the Golden Ratio (AKA Golden Section or Golden Mean) for Artists. Web. 11 Apr. 2016.

 Dauben, Joseph. "Khan Academy." Khan Academy. Web. 11 Apr. 2016. 

 "Techniques of Chinese Brush Painting." Techniques of Chinese Brush Painting. Web. 11 Apr. 2016.
 
 Vesna, Victoria. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." YouTube. Uconlineprogram, 2012. Web. 11 Apr. 2016. 

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