This short report and presentation related to the Golden Ratio. The Golden Ratio has interested mathematicians for a long time. The Golden Ratio is a special number that is defined mathematically from
which produces 1.618033989…, commonly used as the approximation 1.618. There is interesting fact that digits just keep on going to infinity, with no pattern. Mathematically, the Golden Ratio is tends to be an irrational number.
Two numbers tend to be “golden” if the ratio of their sum to the bigger number is equal as the larger to the smaller number. In other words, this relationship could be expressed with the following equation:
In the case of a rectangle, if k is the length of the longer sides, whereas m is the length of the shorter sides,
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Historically, this number can be found in the architecture of many ancient buildings such as the Parthenon and the Great Pyramids. Some investigations of the Acropolis, including the Parthenon, established that majority of its proportions mostly are close to the golden ratio. It could be concluded that architects knew the golden ratio, that is why classical buildings and their elements are proportioned according to the golden ratio. The design of the Parthenon was created according to the Golden ratio, as illustrated in the picture 1. Another famous example of usage the Golden ratio in architecture is the Acropolis of Athens. The dimensions of the Great Pyramid of Giza, which is approximately 4,600 years old, are also based on the Golden Ratio. When it comes to art, there are several illustrations, which can prove that the Golden ratio is used in the arts as well. For instance, Leonardo da Vinci’s paintings in De Divina Proportione (On the Divine Proportion) and Mona Lisa employ the Golden ratio in their geometric equivalents. Also Mondrian used the Golden number in his masterpiece as well as Salvador Dali in his The Sacrament of the Last
In “The Divine Proportion: A Study in Mathematical Beauty,” H.E. Huntley writes about how math is related to basically everything and provides a frame. Math is important to things like art, science, music, and many other things. Huntley was a professor who studied the divine proportion or also known as the “golden ratio.” It is used in math, art, and science.
The Parthenon was an amazing and expensive achievement of ancient Greece. Although it is mostly in ruins today, there is enough knowledge about its construction to allow others to recreate the structure. The Parthenon is often constructed not only to honor the ancient Greeks, but also to honor the culture and place where it is recreated. Although the Parthenon’s influence is tremendous throughout the western world, it is generally only faithfully represented in part- the nearest representations found during my research include the Walhalla and the Nashville Parthenon. This paper focuses mostly on the original building’s history and its influence on American architecture, with a short discussion on a site in Germany. Research was conducted through the use of our course’s textbook, our consortium library, and educational websites. After my research was concluded, I became particularly fascinated with the golden ratio, which is debated to have been used during the construction of the Parthenon. I would like to research this in future work.
The Athenian Greeks at the height of their power built a temple called the Parthenon which was a monument to their core values of perfectionism, humanism, and rationalism. It is important to understand that the human eye has imperfections which deceive the mind, so one can understand the unique steps that were taken to achieve the illusion of perfection to the human eye. The Greeks loved perfection, and as seen in the Parthenon, the Greek architects purposely made the Parthenon imperfect to account for the imperfections in the human eye. This was done so that when one views the Parthenon with the naked eye, it appears to be perfectly symmetrical, straight, and proportional. The entire Parthenon does not have a single right angle. An example of the Greeks compensating for the imperfections of the human eye is seen in the base of the Parthenon, which from a picture or in real life looks perfectly straight, but in reality it is actually curved slightly upward. It is curved because the Greeks knew that if you have a perfectly flat base for a building, it appears curved to the human eye. To account for that, the Greeks made it so that the base was already curved. The Greeks also curved the columns of the Parthenon inward, because if the columns were straight, it would appear to be curving outward. Again, the Greeks knew about how the human eye deceives the mind, and decided that they must trick the eye to please the mind. This was all done because the Greeks strived for
The Athen Civilization was one of the greatest examples of what a flourishing city-state could be. During the Golden Age, Greek civilization was destroyed by an enemy of the city the Persians. At that time, the people of ancient Greece produced amazing architecture. The Parthenon was one of many amazing things created by ancient Greeks. This building was constructed to be a grand symbol of Athens. This building and the surrounding architecture stood for the representation of Greek culture. Some ancient Greek values, beliefs, and skills that are represented by the Parthenon are the belief in being strong, having the most beautiful and grandest architecture and, having the most logical philosophy.
Greek architecture is shown in pillars all throughout the modern world. The most recognizable Greek architecture is located in the image in document 5: the Parthenon. This image shows that the Greeks wanted a city to be represented with artistic value not just with the architecture but also with statues. Another contribution to the Western
The Parthenon is created as an optical illusion. It appears to consist of straight lines but in fact, almost every surface is built to lean and curved from its columns to its foundations. It gives a unique insight into the best that ancient Greek sculptors could produce at the best period of Greek art. The Parthenon is a Doric peripteral temple; it consists of a rectangular floor plan with a series of low steps, and a colonnade of Doric columns. The three main types of columns used in Greek temples and other public buildings are Doric, Ionic, and Corinthian. Many of the sculpture
in architecture of the times. Several elements of the Parthenon follow nature-based models. The rectangular shape of The Parthenon was derived from the Golden Ratio of 5:8, which can be seen in some flowers and nautilus seashells. The drums of The Parthenon?s columns also have natural characteristics. Their diameter is similar to the height of man. Plato?s view of compensation making The Parthenon ?less real? can be contradicted with the nature based models that were used to construct it.
The Parthenon is a beautiful building located in the center of Athens atop of the acropolis. It was built to help Athens become the most beautiful city in all of the Greek city-states. The project of building the Parthenon began in 447 BC by Pericles, the ruler. The structure is more than 200 pous long and 100 pous wide. The Athenians were careful, not to make the building too tall making it appear flimsy nor too wide making it appear squat. The Parthenon is built in one of the three orders used to build buildings in ancient Greece. The order of the Parthenon is called the Doric order. The Doric order is the most simplest and is also the lowest and widest.The Parthenon is a temple that was built to honor the goddess, Athena. Both in and outside
If we look at the Greek temple plan, we can see that they had their frequency of the number of columns. As I mentioned before, they were smart, they had already used mathematic on their buildings. As known as the Parthenon, it is still standing. Some historians found that they had a very great building and sculptural plan. Iktinos and
The Parthenon, currently a museum, was an ancient Greek temple built in honor of the Greek goddess, Athena, whom the Greek people worshipped and revered. It was built between the years 447~438 BC, when the Athenian Empire was as the peak of its power, by Iktinos and Kalikrates and utilized the Post and Lintel architectural system, thus, representing the “tangible and visible efflorescence of Athenian imperial power (“The Parthenon”, n.d.). The Parthenon is often considered as one of the most transcendent works of Greek architecture and I think that its magnificence is a clear indicator of its function to honor the Greek people’s esteemed goddess, Athena. The sheer
Taking multiplication of fractions farther, students in the fifth grade learn how to interpret multiplication by scaling. This is done by saying, “one object is four times as much as another.” For example, if two rectangles are laid side by side it is easy to see how one could be split up in to four pieces while the other stays whole. The rectangle not split up is considered four times bigger than the one split
The Parthenon is known as the Temple of Athena Parthenos. Phidias and his team (Ictinus and Callicrates) began the process of building the Parthenon in 447 B.C.E. “It is one of the main buildings in the Acropolis and was dedicated to honor Athena. The buildings showed a lot of wealth and power to the Athenian empire. The architecture of the Parthenon shows elements of the clarity.” The Parthenon has a rather uniquely structured building. There is nothing cookie-cutter about the shape. The surfaces are rarely straight and there are hardly any completely horizontal or vertical lines. Instead of using the straight lines they went with more of a slight curve. Also the floor was not flat it had a more pronounced curve than people had seen before which made it stand out. The outer floor was had about a 6-inch difference from the inner floor. The unusual structure of the Parthenon was not due to poor architect skills it was completely
Greek architecture was the pinnacle of technology in ancient Greece. The Greeks most distinctive architectural feature was columns. In the Parthenon, there are numerous columns which supported the top. The Greeks were also known for using marble. Many Greek banks, temples and city halls consisted of marble. Why are these techniques used today? Cylinder columns are great for supporting roofs as opposed to any other shapes. Marble is used today mainly for its beauty but is also a strong and expensive material. Another Greek trait in their buildings is symmetry. Humans naturally find beauty in symmetry which is why the world uses symmetric buildings in the majority of its government buildings, banks, and even homes. Overall, the Greeks used marble, cylinders, and symmetry not only to give it an appealing look, but also to give it a good sense of structure and support.
Antoni Gaudi's main inspiration was nature and he implemented it very clearly in his buildings. Gaudi was a religious man and he believed that God exists in nature therefor, he chose nature as his inspiration. He understood that nature is full of curved forms. In his vision, nature can be clarified by geometry and structure which means by understanding the power that gives nature its appearance. Gaudi engaged himself in studying geometry and the structural form, from the human body to the sea and its creatures (Pier, 2010). Sagrada Familia's façades, Gaudi's most famous building, are based on the golden ratio which appears in
The Parthenon was built to express greatness of their influential society and honor the goddess Athena. The Golden Age of Athens is some times referred to as the Age of Pericles, one of the greatest leaders seen throughout our history.