I am celebrating being in Greece this spring break with a few Student Series! blog posts related to the famed civilization of the Aegean Sea. By the way, this student’s blog post was mind-blowing math oriented. He was such an amazing student and a great example about how the “STEM” kids could (& should) involve themselves in the Humanities. Well rounded education for the win!
The Parthenon is one of the most visually pleasing buildings to ever be constructed. The intricate columns and steps may have struggled to survive the test of time, but they towered over Athens with authority. In fact, the Parthenon was such a magnificent creation that many replicas have been built today, one being a full-scale model in Nashville, Tennessee.
As amazing as the Parthenon is, few realize the ways in which math and science were built into the great temple of Athens. The specific ratios and optical illusions that Greeks carefully used give the Parthenon an intangible, but certain, element of beauty.
Greatness through the Golden Ratio
In mathematics, a ratio is an expression of two numbers, or quantities, to one another. So what exactly makes a special golden ratio? To put it simply, a golden ratio can be found when the entire part A is to part B as part B is to part C. The Parthenon was designed with many examples of this golden ratio in mind. For example: the height of the Parthenon from the second step compared to the width, the horizontal and vertical spacing of the illustrations above the columns, and the space between the columns and the roof line all follow the golden ratio. It was no accident that the Greeks built the Parthenon to these exact dimensions.
Golden rectangles, which follow the golden ratio, are often inscribed with a spiral. This spiral, known as the Pythagorean spiral, appears in nature many times over. The golden ratio is thus natural, and the Greeks most likely believed nature was immensely beautiful. Symmetry, another general indicator of beauty, was also common throughout the Parthenon. It’s no coincidence that we think the Parthenon is attractive; it was built to specific and alluring standards.
“Your Eyes Can Deceive You, Don’t Trust Them”
This quote, spoken by Obi Wan Kenobi in Star Wars, is used to instruct Luke on how to use the force. Although no usage of ‘the force’ was necessary to construct the Parthenon, architects had to carefully consider how the human eye and brain would perceive this great building. This consideration led to two noteworthy and unusual patterns showing up in the temple. Firstly, very little straight lines and perfect right angles were actually used in constructing the Parthenon. Secondly, the columns were designed to have a slight bulge at the center.
The reasoning behind these two details lies in the understanding of the human mind’s abnormalities when it comes to visual information. From certain distances, we observe straight lines to be curved. The solution to the Parthenon appearing to lack straight lines was to actually make the Parthenon lack straight lines. Very slight curvature allowed builders to make the Parthenon appear perfectly straight. These optical refinements effectively corrected mental aberrations. As Jeffrey Hurwit stated, “the refinements were made to give the Parthenon an impression of being a living mass that responded to its own weight.” The inclusion of few straight lines and optical illusions illustrates the Greeks’ wealth of scientific knowledge and architectural prowess.
Optical Illusions Continued
So how exactly can straight lines appear curved and vice versa? To begin, all optical illusions prey on the human mind. The optical refinements used in the Parthenon deal mainly with line perception. The Café Wall illusion also deals with how our minds perceive straight lines in specific scenarios. The image included here, and example of a Café Wall illusion, shows “half-shifted” tiles arranged in a checkerboard fashion. The grey “mortar” lines in between the tiles appear slightly slanted, right? The perception of straight or curved lines is one that can thus be manipulated easily. The lines are seen as slightly slanted because of neurons, or nerve transmitters, interacting. Certain neurons react to the white blocks, and other neurons react to the black blocks. As the colors don’t match, there is a minor discrepancy in processing the tiles. These minute discrepancies add up, and the brain sees the line as sloped.
To check out an interactive version of this illusion, head to the following website: https://michaelbach.de/ot/ang-cafewall/index.html. Although the Parthenon obviously isn’t checkered, the scientific principles of tricking the human brain still apply, and certainly were applied in construction of the Parthenon.
- Bach, Michael. “Café Wall Illusion.” Visual Phenomena & Optical Illusions. Updated on December 29, 2015. https://michaelbach.de/ot/ang-cafewall/index.html
- “Café Wall Illusion.” New World Encyclopedia. Modified on March 25, 2013. www.newworldencyclopedia.org/entry/cafe_wall_illusion
- Guan, Kevin Heng Ser. “The Parthenon.” Perspective in Mathematics and Art. Accessed on December 13, 2016. http://www.math.nus.edu.sg/~mathelmr/projects/kh2-urops.pdf
- Jollands, Beverley and Paul Fisher. 100 Landmarks Of The World: A Journey To The Most Fascinating Landmarks Around The Globe. Bath: Parragon, 2011.
- Lewis, Susan. “The Glorious Parthenon.” PBS. Published on January 29, 2008. www.pbs.org/wgbh/nova/ancient/glorious-parthenon.html
- Meisner, Gary. “The Parthenon and Phi, the Golden Ratio.” Golden Number. Published on January 20, 2013. www.goldennumber.net/parthenon-phi-golden-ratio/