Geometry Influences Art
In art there are two directions an artist can go with their work; one focusing on learning and gathering from the past works and theories of previous artists, by studying and appropriating their techniques and styles and effectively improve skill. The other way is to disregard past expressions and focus on the inner source and personal experience, where all the outcome of artwork is original and developed uniquely by the artist.
There is a certain balance between these two influences that makes, in my opinion, effective artwork. Without historical context and references to other past artworks and artist, a unique work can seem out of place or not be clear to the viewer. Without a personal taste and style, where an artist cannot bring their own experience into the work, the work can seem unremarkable, or worse a copy.
Many artists, including me, want to reflect of the essence of art that has developed over the millennia, and classical art has often been a primary source for artists in the western world. Plato and the other Greek philosophers and mathematicians, such as Euclid, Pythagoras, Filius Bonacci, Vitruvius, Socrates and Aristotle are paramount in the understanding of art being present throughout our world, as well as science and all the eccentric patterns that make up our surroundings. They saw a unity or balance in their surroundings, and mathematics was the idealized way to represent it.
The Golden Ratio
A characteristic of living organism, manifestations in our world both at the micro and macro level have been measured and recorded to reveal a pattern ingrained in all of our surroundings. This Golden ratio in which things form has been recognized for centuries, rediscovered during the Renaissance, has held place as a signifier of beauty and is used even to this day, including now in my art.
The Golden ratio, most accurately show in fractions, as 8/5, 13/8, 21/13, 34/21…
commonly recognized as the Fibonacci sequence of 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.
ɸ= 1+ √5 = 1.618
2
Each following number is the addition of the previous two, and equates to the general art rule of thirds.
This ratio manifests in so many places around us that whole lives and books have been dedicated to its mysterious qualities. But for example, the Golden Ratio reflects natural spacing such as the curvature of mollusk shells, the distribution and distance of leaves on plants, in natural formations of five like starfish and in mammal fingers and toes, but it also dominates the constructions of great cathedrals and other masterworks of art and architecture.
In the Geometry of Life and Art by Matilda Ghyka was I finally shown how these math terms translate in a visual way, and the diagrams and figures are very telling. While many of us are taught the fibonnacci sequence in school, this book brings both aesthetic and mathematics together through a common history that explains so much more.
She argues that as for arithmetic numbers, the Golden Section (ratio or Fibonacci sequence) was most significant. Aside from the irrational number of Pi, it had the most significant impact on human endeavors during the time of its discovery. It influenced art and architecture, even to today and within my own studies and art.
Golden Section Droplet
In my past works, the droplets I would draw were generally organic, guided by the space in the drawing, but varying. It did not bother me because, as with life, there are no perfect droplets aside from the idealized one in my head. Each stroke to make a droplet follows what I understand as a droplet shape, an idealized droplet; what Plato would say is the Ideal.
In this study I question what the idealized droplet would be if I could draw it.
Mathematics would be involved and research a helpful tool. The Golden Ratio was the clear plan for idealizing the droplet shape. With the use of Pi, which functions as the base of the droplet, and the Golden Section to determine proper proportions for the droplet, I made several sketches, using Ghyka’s figures (p 11) as guides and then measured out the guide onto a surface.
While I like the idea of each droplet I draw being an attempt at perfection, where method and concentration betters accuracy and measure, I nonetheless appreciate this new idealized shape of the golden ratio droplet.
The golden ratio droplet does a better job of representing the idealized droplet, the one I imagine in my mind, or the one that exists in the meaning of the word. Mathematics and aesthetics seem to be an expression of the same essence and by using both my drawing can be even more impressive.
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Ghyka, Matilda. The Geometry of Art and Life. New York: Dover Publications, 1977.