Unit 2: Math + Art
Richard Buckminster Fuller believed that there exists a genius inside every individual (Vesna Lecture). Living as an engineer, architect, poet, environmentalist, and much more, Fuller juxtaposed science and art in his work and teachings. Mathematics has significantly made its appearance through various artistic forms. In some of M.C. Escher's artwork, for example, the influence of geometric shapes is evident. By combining and intersecting various shapes together, an intriguing visual is produced, all thanks to Escher's interest of and knowledge in geometry.
Another artist influenced by the studies of math is Leonardo Da Vinci, who drew sketch shown below, known as an iconic symbol of both math and art. Some mathematical concepts that likely influenced Da Vinci include linear perspective, symmetry, the golden ratio, and geometric shape. In the drawing, one can note the circle and square used to aid the artist's work and how fitting the proportions of the human body are.
Although the juxtaposition of math and art have been noted throughout history, the relationship has also appeared in popular culture as well. In the film Flatland, the viewer witnesses what it is like to live in a 2-dimensional world. In the film, 3-D laws are difficult to explain to the 2-D inhabitants. In relation to pop culture, the same can be said about the fourth dimension. Perhaps the film is stating that although exploring the fourth dimension is beyond artistic comprehension or desire at times (Henderson), this should not be a valid reason to reject dimensions beyond us. In fact, mathematicians come as assisting players in such conceptual understanding, offering artists the chance to expand on their own subjective understandings. Painter Tony Robbin has claimed that doing so supports "new aesthetic and conceptual capabilities" for artists as he continually finds that "physicists and mathematicians are usually in step [with the artist]" (Henderson).
I find the application of mathematics into art to be one of the most visually-appealing experiences for me as an engineer. Knowing how difficult the derivation of a complex curve can be, I am in awe when such work done on paper can transform visually. The shell shown below is a popular representation of how powerful tools like Wolfram Mathematica can utilize the basic concepts engineers and scientists alike learn in multi-variable calculus.
Sources
Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, pp. 205–210.
“I Always Thought Martin Sheen Was a Bit Two-Dimensional.” Discover Magazine, http://blogs.discovermagazine.com/cosmicvariance/2007/01/25/i-always-thought-martin-sheen-was-a-bit-two-dimensional/#.Ws0qv-jwZPY.
Lee, Xah. “Mathematics of Seashell Shapes.” Mathematics of Seashell Shapes, xahlee.info/SpecialPlaneCurves_dir/Seashell_dir/index.html.
“Mathematics.” Leonardo Da Vinci Mathematics, www.leonardo-da-vinci.net/mathematics/.
"The Mathematical Art Of M.C. Escher". Platonicrealms.com. N.p., 2017. Web.
“Three Intersecting Planes by M.C. Escher.” Curiator, curiator.com/art/m-c-escher/three-intersecting-planes.
Vesna, Victoria. “Math + Art.” Lecture 2. <https://cole2.uconline.edu/courses/888567/pages/unit-2-view?module_item_id=16300792>.
 |
| Three Intersecting Planes by M.C. Escher https://curiator.com/art/m-c-escher/three-intersecting-planes |
Another artist influenced by the studies of math is Leonardo Da Vinci, who drew sketch shown below, known as an iconic symbol of both math and art. Some mathematical concepts that likely influenced Da Vinci include linear perspective, symmetry, the golden ratio, and geometric shape. In the drawing, one can note the circle and square used to aid the artist's work and how fitting the proportions of the human body are.
 |
| Vitruvian Man by Leonardo Da Vinci http://www.leonardo-da-vinci.net/mathematics/ |
Although the juxtaposition of math and art have been noted throughout history, the relationship has also appeared in popular culture as well. In the film Flatland, the viewer witnesses what it is like to live in a 2-dimensional world. In the film, 3-D laws are difficult to explain to the 2-D inhabitants. In relation to pop culture, the same can be said about the fourth dimension. Perhaps the film is stating that although exploring the fourth dimension is beyond artistic comprehension or desire at times (Henderson), this should not be a valid reason to reject dimensions beyond us. In fact, mathematicians come as assisting players in such conceptual understanding, offering artists the chance to expand on their own subjective understandings. Painter Tony Robbin has claimed that doing so supports "new aesthetic and conceptual capabilities" for artists as he continually finds that "physicists and mathematicians are usually in step [with the artist]" (Henderson).
 |
| Flatland (film, 2007) http://blogs.discovermagazine.com/cosmicvariance/2007/01/25/i-always-thought-martin-sheen-was-a-bit-two-dimensional/#.Ws0qv-jwZPY |
I find the application of mathematics into art to be one of the most visually-appealing experiences for me as an engineer. Knowing how difficult the derivation of a complex curve can be, I am in awe when such work done on paper can transform visually. The shell shown below is a popular representation of how powerful tools like Wolfram Mathematica can utilize the basic concepts engineers and scientists alike learn in multi-variable calculus.
 |
| Mathematics of Seashell Shapes http://xahlee.info/SpecialPlaneCurves_dir/Seashell_dir/index.html |
Sources
Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, pp. 205–210.
“I Always Thought Martin Sheen Was a Bit Two-Dimensional.” Discover Magazine, http://blogs.discovermagazine.com/cosmicvariance/2007/01/25/i-always-thought-martin-sheen-was-a-bit-two-dimensional/#.Ws0qv-jwZPY.
Lee, Xah. “Mathematics of Seashell Shapes.” Mathematics of Seashell Shapes, xahlee.info/SpecialPlaneCurves_dir/Seashell_dir/index.html.
“Mathematics.” Leonardo Da Vinci Mathematics, www.leonardo-da-vinci.net/mathematics/.
"The Mathematical Art Of M.C. Escher". Platonicrealms.com. N.p., 2017. Web.
“Three Intersecting Planes by M.C. Escher.” Curiator, curiator.com/art/m-c-escher/three-intersecting-planes.
Vesna, Victoria. “Math + Art.” Lecture 2. <https://cole2.uconline.edu/courses/888567/pages/unit-2-view?module_item_id=16300792>.
I liked how you talked about the films on 2D and 4D and how they relate to the concepts of art and math. I am very curious as to what the film Flatland is like and will definitely look into it!
ReplyDelete