leahnDESMA9: Week 2

From this week’s material I have gained better insight into how art and mathematics are related. I never realized how similar the laws in art, mathematics, and science are to each other or how they intertwine. It's just mind-blowing.

Mathematical patterns are seen everywhere, from nature to the human body to the stock market. Fibonacci's sequence in particular is ubiquitous. ‘Fractal art is a form of algorithmic art created by calculating fractal objects and representing the results as still images, animations, and media.’

Fractals are an artistic example of repetitious patterns in nature and human behavior.

Fractals

Fibonacci Pattern

Humans unknowingly use the golden ratio every day when 'checking each other out'. The golden ratio of the perfect face is amazing in that the human mind creates ratios to determine whether a face is symmetric and thus more visually appealing.

Woodcut from De Divina Proportione illustrating the golden ratio as applied to the human face.

"Euclid's Fifth Postulate," or simply the "parallel postulate", which in Euclid's original formulation is: If a straight line falls on two straight lines in such a manner that the interior angles on the same side are together less than two right angles, then the straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. This fancy postulate added to the science of art by adding mathematical principles to creativity.

4-D

What's even more insightful is how the fourth dimension brings art to life with technology.

4-D and Technology

Buinelleschi(1413) used vanishing points in his creative work. He is credited with the first correct formulation of linear perspective. Since discovering the vanishing point, artists could utilize science and optics to enhance art and make it more realistic and to scale. This seemingly simple concept of proportion and line work transforms flat art into another dimension. As children, most of us drew people standing next to a house without any concept of scale. Thanks to Buinelleschi, we can use proportion, geometry, and vanishing points to transform art.

Buinelleschi

Concept of Vanishing Point

No Dimension or Vantage Point

Vantage Point

Other artists and scientists can use math in a plethora of ways. For example, the art of origami is fundamental in the creation of space telescopes, heart stents, air bags, etc. Origami uses 3-D naturalism, creased patterns, and blueprints that apply patterns of mathematical principles. The four laws are like the laws of quantum mechanics in that they are simplistic in form but greatly impact life as we know it. [2-colorability, at any interior vertex, M-V= +/- 2, alternate angles around a vertex sum to a straight line, no self-intersection at overlaps] Artists can rely on mathematicians, computers, and principles of circles to make complicated, detailed origami that would otherwise be impossible to create.

Origami

Math, art, and science are essential to growth, accuracy, and life. Without math, art woulds still look 2-D; without the number 0 in math, calculations would be incorrect. Each aspect is essential and works together.

Works Cited:

Art and Mathematics

http://en.wikipedia.org/wiki/Mathematics_and_art

Lecture: Buinelleschi

https://www.youtube.com/watch?v=mMmq5B1LKDg

Origami

http://www.ted.com/talks/robert_lang_folds_way_new_origami.html

Fibonacci, Fractals and Financial Markets

http://www.youtube.com/watch?feature=player_embedded&v=RE2Lu65XxTU

The Golden Ratio

http://www.youtube.com/watch?v=GO3o9drC1mQ

Euclid's Fifth Postulate