Math + Art

      Delving further into our discussion of how science and art are intertwined, we had a look at how properties of mathematics appear naturally in our everyday environment. The Fibonacci sequence is a perfect example of naturally occurring ratios in plants, animals, and weather phenomena. Humans have been using the concept of this ‘golden ratio’ to represent a sense of natural aesthetic perfection from the pyramids of Egypt and the Parthenon to the logos for iCloud and Pepsi. Along with this ratio, it should be noted that humans also have a penchant for symmetry. Being symmetrical in our appearance, humans have a natural tendency to use symmetry in nearly all art forms.

[Apple's iCloud logo uses the golden ratio in its design]

      In twentieth century music, radical shifts away from tonality produced a style of music that, quite literally, turned music into numbers. This style came with its own sort of manual called ‘set theory,’ which assigns each of the twelve pitches a number from 0 to 11. Using a modular system with 12 as its base, set theory takes a motif consisting of a ‘set’ of pitches and transforms them by means of reflection, transposition, inversion, etc. to elaborate an idea. This can be applied to certain pieces of composers like Béla Bartók. In the excerpt below, the five notes of the first and second measure contain the same number of whole-steps and half-steps and in the same order ( pitch class set representative: [0,2,3,4,5] ), just symmetrically inverted around an axis and transposed. These algebraic techniques are used to show the symmetry and relationships between sets of pitches.

[first two bars from Bartók's Bulgarian Rhythm No. 155 from Mikrokosmos]

      The interrelationship between art, science, and mathematics is right outside our window. Artists in all cultures are influenced by numbers, whether they know it or not, due to mathematical occurrences in nature. Fractals can be seen in things such as ferns, lightning, and nautilus shells, which then can be found in the braiding of hair in African cultures. People can use properties of linear symmetry to fold paper into origami, capturing the beauty of a crane on the surface of a pond. It all fits perfectly.

 

[Fibonacci sequence occurring naturally]

 Citations:

Eglash, Ron. 'African Fractals'. Ccd.rpi.edu. N.p., 2015. Web. 7 Apr. 2015.

"Fibonacci, Fractals and Financial Markets - Socionomics.net." YouTube. YouTube, 31 May 2007. Web. 9 Apr. 2015.

Hart, Vi. "Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]." YouTube. YouTube, 21 Dec. 2011. Web. 9 Apr. 2015.

Lang, Robert J. "Huzita-Justin Axioms." Huzita-Justin Axioms. Web. 9 Apr. 2015

Lefkowitz, David. Analysis of Post-Tonal Music: A Parametric Approach. N.P., 2014. Print.