1.618

Growing up we usually start to distinguish ourselves artistically, intellectually, or athletically throughout the first few years of school.  Some people say that the right versus left side of the brain being used is the primary division between the artistic and the intellectual.  But is there truly a hard line between the two aptitudes? or is the boundary blurred a bit?

1 to 1.618 is the relationship between two lengths defined as the golden ratio.  The golden ratio is represented naturally in countless situations.  The most commonly known example is the shape and relative proportions of the concentric spirals of a shell.  Starting from the first square in the shell illustration, each following square is of the 1:1.618, or golden, ratio.

The golden ratio is significant because artists use this mathematical relationship to tie together the world of numbers and the world of art.  In the painting Mona Lisa, squares similar to those seen in the shell illustration are used to outline how DaVinci used the most natural-looking and beautiful proportions.

"For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art," M.C. Escher once said of his own artwork.  In the case of Maurits Cornelis Escher (M.C. Escher), the afore mentioned boundary is blurred through ink.  He uses geometry and the mathematical structures of tessellation to create eye-alluring mind puzzles.

Through years of conditioning, we have learned to see the worlds of art and math as distant and unrelated. However, as technology develops, we see more and more the boundary blurring.  Digital art is slowly popularizing and what is digital art if not specifying pixel size, dropping, and morphing shapes on a mathematical grid?  

Right-brainers see art as unruled expression-and maybe it feels like it with pencil in hand-but artists are intentionally and unintentionally using the rules of ratios and geometry to formulate the perfect image.  

Resources:
"Mathematical Art of M.C. Escher -- Platonic Realms MiniText." Platonic Realms Entryway. Web. 14 Oct. 2013. <http://www.mathacademy.com/pr/minitext/escher/>.

"Definition of Golden Ratio." Math is Fun - Maths Resources. Web. 14 Oct. 2013. <http://www.mathsisfun.com/definitions/golden-ratio.html>.

"15 Uncanny Examples of the Golden Ratio in Nature." io9 - We come from the future. Web. 14 Oct. 2013. <http://io9.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature>.

Obara, Samuel. "Golden Ratio in Art and Architecture." Jim Wilson's Home Page. Web. 14 Oct. 2013. <http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html>.

"Verbal vs. mathematical aptitude in academics - Gene Expression | DiscoverMagazine.com." Discover Magazine Blogs. Web. 14 Oct. 2013. <http://blogs.discovermagazine.com/gnxp/2010/12/verbal-vs-mathematical-aptitude-in-academics/#.Ult2jhZcuTE>.