Week 2 - Art&Math

I found it incredible that so many ancient artists incorporated mathematics into their works such as Albrecht Durer. He pioneered a new era of perspective and shadowing using mathematics he learned while in Italy. He learned of ideal proportions such as the golden ratio, and coupled this calculated style of art with shadowing techniques to create aesthetically pleasing, ideal organic structure. 

"The Four Horsemen of the Apocalypse"
by Albrecht Durer

Take Durer's famous painting, "The Four Horsemen of the Apocalypse," where shadows, linear perspective, natural and artificial perspective, and horizontal lines are all used to convey depth, size, proportion, and overall natural realism. The degree of overlap between the different horses creates a line aimed towards a back-right point. Other parts of the artwork such as the sword, bow string, falling victims, and the backs of the horsemen all send parallel lines towards this same convergent spot, once again using geometric angles to create an optical perspective.

Infrastructure example of the "Golden Ratio" in the Parthenon

Biological examples of the "Golden Ratio"

Fractals, spirals, and the Fibonacci sequence all follow this same type of organic proportional increase, but it's truly fascinating how this golden ratio of Phi is noticeable in so many aspects of our natural and artificial lives. Anything from shells and hurricanes, to financial oscillations and infrastructure follow these sequences. Such aesthetically pleasing and common structures couldn't be a coincidence, and it turns out they aren't! The reason for these particular sets of proportions taking over our daily lives is because these are the most efficient patterns of growth and extension. Since the golden ratio happens to be the most efficient way for biological systems to operate, evolution has taken its course to express this golden proportion in many systems. Likewise, CEO's try to model their companies through this ever increasing series as best as they can to maintain this perfected system of growth. 

There really isn't as much juxtaposition between the fields of art, science, and math as I originally believed. In fact, they are actually very interrelated from a fundamental standpoint as shown by the golden ratio. As professor Vesna spoke of in her lecture, the juxtaposition comes from society's belief that art and science are two polar opposite fields of study, as well as society's subsequent decision to isolate these fields from one another while we are just starting our education. Which is why we are unfortunately never exposed to these two subjects in tandem at a young age.

Sources

 "Albrecht Durer - The Complete Works." Albrecht Durer - The Complete Works. Creative Commons License, Jan. 2002. Web. 10 Apr. 2016.

Banker, Teresa. "Biological Connection to Golden Ratio." Biological Connection to Golden Ratio. Web. 10 Apr. 2016.

Pierce, Rod. "Golden Ratio" Math Is Fun. Ed. Rod Pierce. 27 Dec 2015. 11 Apr 2016

 Rose, Vicky. "The Golden Ratio: A Brief Introduction." Totem Learning. 22 Apr. 2015. Web. 10 Apr. 2016.

Vesna, Victoria. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." YouTube. Web. 10 Apr. 2016.