Math and Art

In this week’s lesson I learned that origami has a lot more involved to it than just folding paper. Origami started out as the traditional Japanese art of paper folding and has now become a modern art form. Due to the constrictions of straight edge paper folding, origami is both mathematically interesting and beautiful.

http://www.langorigami.com/science/math/hja/hja.php

Robert J. Lang states that the Huzita-Justin Axioms were the “first formal description of what types of geometric constructions were possible.” These axioms are seven different ways in which one could fold a single crease by aligning one or more combinations of points and lines on a paper. It was mathematically proven that there are only these seven axioms. Paper folding can solve arbitrary cubic equations, angle trisection, and doubling the cube. Paper folding has become very influential in mathematics, but the mathematics has also helped make unique sculptures out of a single sheet of paper.

http://mars.wne.edu/~thull/papers/amer.math.monthly.118.04.307-hull.pdf

Through certain crease patterns, Lang is able to create intricate designs of animals out of paper. Lang has created various methods that provide structural information in his designs. In TreeMaker, origami was no longer just folds, the underlying data contained many linear features. These were considered paths and each path would state whether the path of the fold would work in creating the final design.

 http://www.architecturaldigest.com/blogs/the-aesthete/2012/04/geometric-patterns-islamic-art

Another case in which math is used in art is with Geometric Pattering. Geometric pattering is found in a lot of Islamic historical sites such as mosques. Geometric patterns were used to track the stars as well as improve acoustics in these areas. A lot of times geometric patterns were used for religious purposes. Human figures could not be drawn on walls for fear of idol worship. Therefore, Islamic structures feature both geometric and nature inspired art.

http://facultyfp.salisbury.edu/despickler/personal/Resources/TechnologyWorkshops/ScienceNight2011/ScienceNightSU.pdf

Mathematics is at the foundation of everything. It has and is being used to create new type of artwork and evolve others. For example, anamorphic art uses angle of perception and only at a certain vantage point can a person see the image. This art form is being used by modern artists to create 3-D allusions on sidewalks and has gained much popularity. These art forms are influential in culture, mathematically interesting, and aesthetic. Math has bridged the connection between art and science and with every new insight becomes inseparable.

http://www.huffingtonpost.com/2012/08/08/3d-street-art-optical-illusions-chalk-artists_n_1757390.html

Sources:

Thomas C. Hull (2011, April). Solving cubics with creases: the work of Beloch and Lill. The American Mathematical Monthly ,118, 307-315.

Gates, Sara. "3D Street Art: 13 Amazing Optical Illusions Created By Chalk Artists (PHOTOS)." The
Huffington Post. TheHuffingtonPost.com, 08 Aug. 2012. Web. 13 Oct. 2013.

Owens, Mitchell. "The Aesthete: Exploring Geometric Patterns in Islamic Art." Architectural Digest. N.p., 12 Apr. 2012. Web. 13 Oct. 2013.

Lang, Robert J. "Huzita-Justin Axioms." Robert J. Lang Origami. N.p., n.d. Web. 13 Oct. 2013.

Masarelli, Nicole. “Mathematics Behind Anamorphic Art.” Salisbury University. PowerPoint. 26 March 2012. 13 Oct 2013.
<http://writingcenter.gmu.edu/resources/summaryvsinterpretation/index.htm>.

The Crevasse - Making 3-D Street Art. YouTube. N.p., 15 Feb. 2009. Web. 13 Oct. 2013. <https://www.youtube.com/watch?feature=player_embedded&v=3SNYtd0Ayt0>


Images:

Digital image. N.p., n.d. Web. 13 Oct. 2013. <http://www.webdesignburn.com/wp-content/uploads/2012/06/Origami-peacock.jpg>

Digital image. N.p., n.d. Web. 13 Oct. 2013. <http://www.langorigami.com/image.php?image=/art/creasepatterns/creasepatterns_art/moma_on_wall.jpg&width=300>

Digital image. N.p., n.d. Web. 13 Oct. 2013. <http://www.islamic-architecture.info/WA-TU/800px-Selimiye_Mosque%252C_Dome.jpg>