WEEK 2 - Math + Art

Week 2 - Math + Art 

When we think of art, we rarely consider mathematics playing a role. Yet, math can be seen in various art forms as discussed in this week’s material. This week’s lecture provided me with insight on how math is used in art in regards to perspective. Perspective, brought by Al-Haytham, is the mathematical system for representing three-dimensional space in a flat plane (Vesna). Artists are capable of drawing depth and using linear perspective to go beyond the one-dimensional aspect. Artist, Brunelleschi, was able to do this while also considering the concept of scale—an object’s length in relation to the length of the whole picture (Vesna).

Learning the use of perspective and scale, I began to consider these concepts within paintings such as “Under the Wave off Kanagawa” by Japanese ukiyo-e artist Hokusai. Mathematics can be found within this painting as well, especially with the use of perspective with the mountain in the background, along with the curvature of the waves to appear three- dimensional (Harris).

"Under the Wave off Kanagawa" use of perspective and geometry from Interactive Mathematics. 

I had not considered math within other art forms such as music prior to this week’s lesson. More specifically, after reviewing Music and Computers, I learned how sound is essentially the mathematical concept of functions. A function requires an input and output which then plots lines in the x and y axis of a graph similar to how sound waves are measured by time (input) and amplitude (output) (Music and Computers). Similarly, math is a relationship of codes and patterns and these can be reflected into art themselves. Nathan Selikoff showcases these patterns in audiograms that are visual representations of sound frequencies. Therefore, when a song is created as a form of art, it is not free of math, but our ears are listening to frequencies found in math. 

Sample movement of the waveform from Music and Computers.

Examples of function graphs, in comparison to soundwaves above from Quizlet.

Such as math can be found within paintings and music, it made me interested in further researching whether math is applied in cinematography which I consider another form of art. According to cinematographer, Gordon Arkenberg, math can be applied to cinematography through exposure, optics, photometry, and depth-of-field. For example, in terms of optics, geometry is used to calculate angular field of view—where objects are located in the camera lens. As math can be seen within these three types of art forms, it raises the question as to why art and math are continuously detached from each other when math is essential to the creation of art.

Example of optics and use of math in cinematography from John Arkenberg.

Resources: 

Arkenberg, John G. “Where Is the Math in Cinematography...” Gordon Arkenberg, Gordon Arkenberg, 12 Jan. 2016, http://www.gordonarkenberg.com/blog/2016/1/10/where-is-the-math-in-cinematography.

“Audiograms - Interactive Software Art, Print.” Nathan Selikoff, 18 Jan. 2020, https://nathanselikoff.com/works/audiograms.

“Chapter 1: The Digital Representation of Sound, Part One: Sound and Timbre.” Music and Computers, http://musicandcomputersbook.com/chapter1/01_01.php.

Harris, Leila Anne. “Under the Wave off Kanagawa (The Great Wave) by Hokusai (Article).” Khan Academy, Khan Academy, https://www.khanacademy.org/humanities/ap-art-history/south-east-se-asia/japan-art/a/hokusai-under-the-wave-off-kanagawa-the-great-wave#:~:text=Under%20the%20Wave%20off%20Kanagawa%20is%20full%20of%20visual%20play,snow%20falling%20on%20the%20mountain.

Vesna, Victoria. “Mathematics-pt1-Zeroperspectivegoldenmean.mov - YouTube.” Youtube, UC Online, 2012, https://www.youtube.com/watch?v=mMmq5B1LKDg.

Images:

Bourne, Murray. “Math in Art - Hokusai's ‘The Wave’ - Interactive Mathematics.” Interactive Mathematics - Mathematics, Learning, Computing, Travel - and Whatever... , 23 Sept. 2015, https://www.intmath.com/blog/mathematics/math-in-art-hokusais-the-wave-595.

“Chapter 1: The Digital Representation of Sound, Part One: Sound and Timbre.” Music and Computers, http://musicandcomputersbook.com/chapter1/01_01.php.

 Basic Mathematical Structures Flashcards | Quizlet. https://quizlet.com/gb/469950223/basic-mathematical-structures-flash-cards/.

Arkenberg, John G. “Where Is the Math in Cinematography...” Gordon Arkenberg, Gordon Arkenberg, 12 Jan. 2016, http://www.gordonarkenberg.com/blog/2016/1/10/where-is-the-math-in-cinematography.