Week 2 - Mathematics and Arts

This week's topic is the relations between Mathematics and Arts. In the lectures, Professor Vesna speaks about how mathematicians and artists use arts and math respectively to improve their work. I have learnt that mathematicians, whom we stereotypically consider to be some of the most logical but least artistic people in the world, actually gain many inspirations from arts. For example, Al Haytham, in his book of Optics relates scientific methods, optics and arts together. Heavily influenced by Al Haytham, another scientist, Alberti, relate geometry to the science of optics in his treaties on paintings. Other instances of arts used in science may be seen as in the pavieto, a type of Cartesian system that create a grid to obtain the correct shape of a circle. It was also in this period that the vanishing point rule was made by Brunelleschi in 1413. Later, Piero Della Francesca, a famous artist and mathematician of his time, proposed the theory that painting has 3 parts: drawing, proportion and coloring. By the time of Leonardo Da Vinci, geometric examples are often used to supplement numerical calculations. Another interesting concept is the Golden Ratio and Da Vinci's Vitruvian man, both are perfect examples of symmetry and geometry used in architecture. The Golden Ratio is named by the Greeks and first used by Egyptians in pyramids. Vitruvian man is based on perfect human proportion and shows the geometric relationship between human body and the space we are in, including architecture.

http://kaplanpicturemaker.com/tips__info/golden_rectangle

Leonardo da Vinci's Vitruvian Man

http://kaplanpicturemaker.com/tips__info/golden_rectangle

Personally, I found Robert Lang's artwork very intriguing. Prior to reading through his website, I have never thought of origami as a subset of mathematics, not to mention that there are underlying laws of origami. For example, the Huzita-Justin Axioms describes an extremely restrictive style of folding, when only one fold at a time is permitted. Whereas "two-fold axiom" renders solution to more complex folding problems. There are also branches of related science, such as computational origami and related industrial designs. The juxtaposition of mathematics, art, and science is that by using math, artists may enhance their design and bring it to a new, complicated level that is hard to be imagined by human brain. 

http://www.langorigami.com/art/gallery/gallery.php?tag=human-figures&name=orchestra

Through this week's material, I have not only started to seriously think of the linkage between mathematics, arts and science, but also try to consciously apply arts to statistical concepts in the future because imagination is of imperative importance to mathematical thinking and innovation. In the "Flatland", the flatlanders cannot imagine a three-dimensional world. Similarly, in learning statistics, it is impossible/very hard to for me to imagine a higher level or a totally new applications of the concepts. Artistic thinking frees one's mind boundary and help people to imagine what they cannot see right now, and thus come up with creative solution to current problems. Therefore, it is imperative to incorporate arts and mathematics together when one approaches problems.

http://www.polydi.com/parents/parents.html

Sources:

Abbott, Edwin. “Flatland: A Romance of Many Dimensions.” N.p., n.d. Web. 12 Oct. 2012. <https://cole.uconline.edu/content>.

Robert, J, Lang. “Robert. J. Lang Origami” N.p., n.d. Web. 12 Oct. 2012. <http://www.langorigami.com/>.

Vesna, Victoria. “Mathematics-pt1-ZeroPerspectiveGoldenMean.mov.” Cole UC online. Youtube, 9 April 2012. Web. 11 Oct. 2012. <http://www.youtube.com/watch?v=mMmq5B1LKDg&feature=player_embedded>

Robert, J, Lang. "The Math and Magic of Origami",  N.p., n.d. TED Talk, Feb 2008. <http://www.ted.com/talks/robert_lang_folds_way_new_origami>