The Golden Ratio

Often times, students ask themselves, “How will this apply to me in the real world?”, or  “I never use math, why do I have to learn this?”. Doubt may exist about the usefulness of mathematics, but there is no evidence that supports this doubt. As a student studying math in higher education, I know that math is all around us. I know that everything relies, and consists of some form of mathematics. The most prevalent discovery of math, that is both commonly seen, and unseen, is the Golden Ratio.  The reason I say the Golden Ration is the most prevalent, is because it can be found in nature, science, architecture, and most other aspects of life.

The golden ratio is a number found by dividing a line into two parts, say A and B. The segment A would be longer than segment B, and when A is divided by B, it is equal to the whole length of the line divided by A. The golden ratio is numerically defined as the number 1.6810339887498948420…., and continues on into infinity. It is also represented by the greek letter phi. The golden ratio has been found in nature, and the physical universe. It is not known when it was first discovered by mankind, but can be seen in the works of man dating from ancient times.

The human face is an example of how the golden ratio can be found in nature. When looking at the face, the mouth and nose are positioned in between the eyes and the chin, which represents a golden section. A “perfect” face will have golden proportions between the length and width of the face, the length of the lips and the width of the nose, and the distance between pupils and the eyebrows. Even though all humans are unique, the average of these distances between features is close to phi. It has also been said, that the closer ones features adhere to phi, the more “attractive” society finds them. The reason being, as originally stated, is because the golden ratio is thought to be the most pleasant to the eye. We can even find the golden ratio in our DNA. The molecules in our DNA have been measured to be 34 angstroms in length, and 21 angstroms wide at each full cycle of its double helix spiral.

Parthenon, Athens, Greece The Parthenon without tourists! Athens, Greece (1989/379) From flickr.com, posted by GothPhil

Architecture is another place where the golden ratio is put to use. One example is the Parthenon, found in Athens, Greece. The length and height of the structure,  the spacing between the columns, and the tip of the roof are all contained in the golden ratio. Within the building many golden rectangles can be found as well. The dimensions of the Great Pyramid of Giza, in Egypt, is also based off the golden ratio. The Egyptians believed the golden ratio to be sacred, and it was an important part of their religion. For the Pyramid of Giza, the ratio of the height of the slant compared to one half the length of the base, is the golden ratio. In modern architecture, the golden ratio still applies. In Toronto, Canada stands the CN tower. The CN tower is the tallest freestanding structure in the world. The observation deck of the tower is found at 342 meters, where the total height is 553.33 meters. This ratio between these two lengths is 0.618, or phi.

Not only is the golden ratio used for architecture and design, but also for beauty. Artists for centuries have applied the golden ratio to their work to create the most beautiful pieces of art known to the world. These examples are found in pieces such as The Last Supper by Leonardo Da Vinci, the ceiling of the Sistine Chapel by Michelangelo, and Bathers by Seurat. In the painting of The Last Supper, Leonardo Da Vinci used the golden ratio determine where Christ would sit in relation to the table, and his apostles, as well as, the proportions between the walls and the windows. The golden ratio can be found on the ceiling of the Sistine Chapel where the finger of God, and the finger of Adam meet.  This point, is found by taking the ratio of the height, and width of the area that they are contained in. All of these works of art apply the golden ratio to convey the most realistic shapes and dimensions.

The next time someone says that math does not apply to them or the real world, I would simply suggest they look in the mirror, or visit the nearest museum. The golden ratio can be found in all aspects of life, and will continue to be used to improve the beauty of our surroundings. As humans, we desire organization and structure in our lives. Math provides such needs, and the golden ratio is just one method that is used universally.

Sources:

https://www.dartmouth.edu/~matc/math5.geometry/unit2/unit2.html#Great Pyramid

http://www.geom.uiuc.edu/~demo5337/s97b/art.htm

http://www.goldennumber.net/art-composition-design/

http://io9.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature

http://jwilson.coe.uga.edu/emt668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html

http://www.livescience.com/37704-phi-golden-ratio.html

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