Geometry is used in everything in the world around us, it is even in places that you would not think possible or is used in ways that you would not think necessary or practical. The golden ratio,1:1.61, is a ratio that is used to build, design, structure, and even decorate houses. Most houses that follow the golden ratio, 1:1.61, to the exact all look almost the exact same, even though they may vary slightly. The golden ratio appears in everything in nature, from the shape and structure of clouds, the shape and structure of our universe that we live in, to the proportions of the human anatomy and body. No matter what the eventual purpose of the structure whether it is man made building or objects, or another wonderful creation of mother nature like flamingos or clouds, there is a good chance that it follows or was created by using the golden ratio. …show more content…
From artwork and mathematics, to building houses and even music. There is extreme variation in the use of the golden ratio throughout time, and the golden ratio, 1:1.61, has sunk its roots deep into the fundamental principles of architecture. Many believe that the golden ratio, 1:1.61, also known as phi, dates all the way back to the Ancient Egyptians great pyramids in Ancient Egypt. The golden ratio, 1:1.61 is also commonly found in many large and ancient buildings of the past. For example, the Pantheon in Greece, the Notre-Dame of Laon Cathedral in France, and the Taj Mahal in Agra, India. These great, ancient, and majestic buildings all show a large use of the golden ratio, 1:1.61, also known as phi. For the Pantheon, which was built in 126 AD by the ancient greece, it is the columns that stand out for the exquisite use of the golden
Pantheon and Hagia Sophia Pantheon and Hagia Sophia are two extremely outstanding architectural pieces of their times. They have been built according to the traditions of those particular times. The materials used to built these buildings and the purpose for which they were used are all very important aspects and have been briefly covered in this report. Pantheon The statesman Agrippa built pantheon in 27 B.C. Then it was completely rebuilt by the emperor Hadrian. The Pantheon is remarkable for its size, its construction, and its design. The dome was the largest built until modern times. The present structure was probably originally built as a temple for all the pagan gods. We do hear of it as being a law-court and a reception area for Emperor Hadrian meeting his quests too. Some say that the rotunda of the building was once a Roman bath. Due to all this mystery, the Pantheon is often referred to as the Sphinx of Rome. The visitor will probably not appreciate the construction as much as the Flavian amphitheatre, but it is still a great masterpiece of engineering and well worth a visit. Most Roman and Greek temples at the time of the Pantheon's construction were large, colonnaded, rectangular enclosures with sanctuaries situated in their centers. The Pantheon was different. It consisted of a large circular drum topped with a hemispherical dome. It is a masterpiece of both engineering and art a lasting memory of Ancient Rome’s might. Roman architecture is architecture of wall and enclosed tactile space. Individual column with entablature is no longer the basic architectural unity. Spatially, it shows a development from closed, simple space units and regular articulation to more complex spatial relations, more fluid interpenetrati...
In 118AD, emperor Hadrian completely remodeled the pantheon and saw that it was rebuilt. Construction was completed in 128AD. Emperor Hadrian loved architecture, but he was no architect himself. It is believed
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
The foundation of Greek culture was balance, reason, and harmony which can be unveiled in their art. As the civilization heavily revolved around religion, massive temples were built to serve the Gods. Greeks believed in many Gods, meaning they had polytheistic views . This notion of polytheism passed down to the Romans who adopted nearly the exact same deities and built similar architecture as well. One of the most famous buildings of worship was the Greek Parthenon built around 447-432 B.C.E, worshipping the goddess Athena . While building these brilliant pieces of art, concepts regarding laws and the natural world from philosophers were being incorporated in the structure. Pillars were often built in temples and various buildings in both Greek and Roman cultures. Doric, ionic, and Corinthian stand as the main three pillars built; each of them becomes increasingly more elaborate by order. For example, the Corinthian was the most intricate. Romans quickly developed a taste for this form of architecture and incorporated into theirs later on. The Romans however were very inventive, and began to develop the arch, vault and dome to add to what they emulated from the Greeks. Using these elements the Romans built what is known as the Coliseum, built over a 10 year span from around 70 AD to 80 AD. The Coliseum was said to hold 50,000 spectators and was used for entertainment
As one of the greatest structures in Rome, the Pantheon was built between 118 and 128 CE. It is described as the most remarkable ancient building surviving in Rome. After being destroyed and rebuilt twice, it was renamed the “Temple of the Gods”. In 126 AD, the Pantheon was restored to its glory, by the architects who at that time has learned and mastered their craft in concrete construction in the Greek Classical order. They constructed a massive 25 foot thick walls which was to support the huge dome made of concrete to be placed at the top. The dome was the largest ever made of unreinforced concrete at 43.4 meters in diameter (Matthews, Roy and Platt pg. 5).
Nevertheless, that day followed me, and I tried to understand more about fractals through the resources I already had at my disposal-- through courses I was taking. Sophomore year, through my European History and Architecture courses, I learned about many ancient architectural feats-- Stonehenge, the Pyramids of Giza, the Parthenon, many Gothic Cathedrals, and the Taj Mahal-- and that they all somehow involved the use of the golden ratio. I will come back to how this relates to fractals later in the article, but for now know that each of these buildings use different aspects of their design to form the golden ratio. I was intrigued by the fact that fractals, what seemed to be something only formed by the forces of nature, were being constructed by human hands. Although I wanted badly to find out more, I waited until that summer, when I discovered a YouTube account by the name of Vihart. Vihart’s videos are not tutorials on how to do math, however Vihart’s ramblings about the nature and the concepts of the mathematical world have a lot of educational value, especially on topics that are more complicated to understand then to compute. Her videos on fractal math and their comparability to nature, helped to show me that...
Greek palaces and temples, consisting of massive columns, were built for the gods or other religious purposes. The temples found at the center of the polis, the acropolis, were made as earthen dwellings for the gods, a place for storage of sacred objects and offerings, and also served out tasks for the polis such as keeping records. Temples, along with other sacred places were sometimes only open to certain peoples or cults, and people who were not ritually purified or had “religious pollution” were not allowed to enter sacred places (Adkins & Adkins 338). The fact that the religion centers are in the middle of the cities symbolizes how Greek religion was central to Grecian life, it was one of the most important things to them. The temples also represent the architectural and cultural achievements of the Greeks. The magnificent style of these temples has influenced not only Greece but the whole world as Grecian columns have been a staple in architecture since there creation; this is even evident in the United States with buildings such as the United States Capitol, built hundreds of years after the establishment of Ancient Grecian architecture. Along with architecture, Greek art, most notably pottery and sculpture, was also influenced by religion. Greek pottery, depicting mythological and heroic scenes, and statues, portraying the human form often made in the image of gods,
When you draw a quadrant in each square a spiral is formed, which is identical to the shells of snails and nautilus. This Fibonacci spiral can also be found in human ears, spiral galaxies, hurricanes, cauliflowers, pineapples, sunflower and each of those spirals in plants contains a number of seeds, florets, bumps or leaves that are equal to a Fibonacci number. Furthermore, when one number of the sequence is divided by the previous number and as the number increases, the result approaches 1.618, getting increasingly accurate, but never quite reaching that ratio. This ratio is known as The Golden Mean or The Devine
The Parthenon was built during the Golden age in Athens, Greece. The Parthenon is made of mainly columns; there is a 9:4 ratio. It was almost destroyed in war; the ruins that remained were dedicated to Athena. The purpose of the Parthenon was to house the statue of Athena, made of ivory and gold, and also Athena’s treasure. The ratios and the equations used to make the Parthenon were used as a sign of the harmony in the natural world around us. The mathematical harmony in the world shows how we can work with the world rather than destroy to make it what we want. The Parthenon also has no straight lines. The columns of the Parthenon are angled going up getting smaller the higher they get. This was done so that you could get the best lighting
Throughout history, there have been several significant architectural movements. The last, and perhaps most enduring movement is that of Classic Greece. Although for centuries, the architecture of ancient Greece has been admired, mimicked, and replicated, its beginnings are somewhat surprising to one unfamiliar with the history of the region. It is important to understand the history and mechanics of Classic Greek architecture in order to fully appreciate its form, function, and beauty. “Ancient Greek architects strove for the precision and excellence of workmanship that are the hallmarks of Greek art in general. The formulas they invented as early as the sixth century B.C. have influenced the architecture of the past two millennia” (metmuseum.org).
The ancient Greeks developed a system of orders which were known as columns. There were three different types of columns and each had they own special twist, both structurally and appearance wise. The three orders consisted of the Doric order, Ionic order and the Corinthian order. One shocking fact was that the Romans used the Corinthian columns more than the Greeks did and they were the one that came up with them. Each order could be found in many different parts of ancient Greece. The columns were put into use by creating ancient temples. Since Greek life was mainly focused around religion, their temples were very big and beautiful (“Ancient Greece” 1).
In Ancient Greece, religion dominated their life, so it is understandable that their architecture would be dominated by their religion. Before Greece became many different city-states, they had kings, and they would build a room called a megaron to show they King’s authority. A typical megaron is a single chamber with a fire pit in the middle with a throne off to the side. This room opened up into a porch (portico) that had four columns in the front. After there were no more kings these megarons turned into temples. The fire pit, which turned into some type of altar or a place to show a sacrifice for that god, was now outside in front of the temple. The altar was now outside so people could see you make these sacrifices to their gods. The first Greek temples were made out of wood and were long rectangular buildings with a porch all the way around which was supported by columns made from tree trunks. A Greek temple consists of five basic parts: the pediment, entablature, columns, base, and the cella, or the inner sanctum. The pediment is triangular and would have a type of sculpture or ornament known as acreteria on each corner. An entablature consists of three parts: the cornice, frieze, and architrave, which holds up the pediment. The columns are the support between the entablature and the base. The base usually consists of three steps. The cella is the inner sanctum, which has different rooms with more columns for support. Each temple would have a cella but they were not identical.
...on of light and the rays are proportions in the Fibonacci sequence. Fibonacci relationships are found in the periodic table of elements used by chemists. Fibonacci numbers are also used in a Fibonacci formula to predict the distant of the moons from their respective planets. A computer program called BASIC generates Fibonacci ratios. “The output of this program reveals just how rapidly and accurately the Fibonacci ratios approximate the golden proportion” (Garland, 50). Another computer program called LOGO draws a perfect golden spiral. Fibonacci numbers are featured in science and technology.
The golden ratio is a term used to describe proportioning in a piece. In a work of art or architecture, if one maintained a ratio of small elements to larger elements that was the same as the ratio of larger elements to the whole, the end result was pleasing to the eye.
A rectangle is a very common shape. There are rectangles everywhere, and some of the dimensions of these rectangles are more impressive to look at then others. The reason for this, is that the rectangles that are pleasing to look at, are in the golden ratio. The Golden Ratio is one of the most mysterious and magnificent numbers/ratios in all of math. The Golden Ratio appears almost everywhere you look, yet not everyone has ever heard about it. The Golden Ratio is a special number that is equal to 1.618. An American mathematician named Mark Barr, presented the ratio using the Greek symbol “Φ”. It has been discovered in many places, such as art, architectures, humans, and plants. The Golden Ratio, also known as Phi, was used by ancient mathematicians in Egypt, about 3 thousand years ago. It is extraordinary that one simple ratio has affected and designed most of the world. In math, the golden ratio is when two quantities ratio is same as the ratio of their sum to the larger of the two quantities. The Golden Ratio is also know as the Golden Rectangle. In a Golden Rectangle, you can take out a square and then a smaller version of the same rectangle will remain. You can continue doing this, and a spiral will eventually appear. The Golden Rectangle is a very important and unique shape in math. Ancient artists, mathematicians, and architects thought that this ratio was the most pleasing ratio to look at. In the designing of buildings, sculptures or paintings, artists would make sure they used this ratio. There are so many components and interesting things about the Golden Ratio, and in the following essay it will cover the occurrences of the ratio in the world, the relationships, applications, and the construction of the ratio. (add ...