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Short essay on Euclid geometry
Story of human evolution
Story of human evolution
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In the field of art, artists always use techniques and methods to make their work better. The ‘Rule of Thirds’ and The ‘Golden Ratio’ are amongst the most important techniques in artwork. The ‘Golden Ratio’ is an ancient mathematical method. Its founder is the ancient Greek Pythagoras. (Richard Fitzpatrick (translator) ,2007. Euclid's Elements of Geometry.) The ‘Golden Ratio’ was first mentioned 2300 years ago, in Euclid's "Elements" .It was defined as: a line segment is divided into two sections, ‘a’ and ‘b’ as shown in the diagram below ,when the ratio of a:b is equal to the ratio of a+b:a , the ratio is perfect. The ratio is 1.6180. The ‘a’ occupy for the 0.618 of the ‘a+b’. (Richard Fitzpatrick (translator) ,2007. Euclid's Elements …show more content…
It was found that almost all paintings, sculptures and photographs main body was the position of 0.618. The golden ratio and the golden rectangle can bring the beauty to the picture. In fact, there is no exact explanation why the 0.618 is the perfect proportion. However, some people infer that In the process of human evolution, the body has a lot of ratio close to 0.618. Because people at that time did not have a definition of beauty, they only feel that the proportion of their own body is beautiful. So it is considered to be the most perfect ratio until today. The golden ratio can be found in many artworks in nature. Athens Greek temple of Parthenon is a good example of Finch's "Vitruvian Man" with the golden rectangle. "Mona Lisa" is also in line with the golden rectangle, "The last supper" also applies the proportion of the …show more content…
If her head is fixed in a rectangular box , the rectangular length to width ratio is 2:3. The ratio is equal to 0.618. In addition,her head and body proportions are also 0.618. Next case is David .Artists found that according to 0.618:1 to design the length of the legs and the height of the proportion of the body. The navel as the dividing point. The figure is the most beautiful. So, Michelangelo created David,the role of the golden ratio is that the sculpture looks more
This invention distinguish his David from any other David Statue before him. At Bernini’s ear, David was a popular subject in Italy. At that time Italy did not have a powerful central government, and cities were seeking for their independence. The story of David killed Goliath and won the independence of Israel was understand as a symbol of independent. Therefore the statue of David also had political meanings. The two most famous David were from Donatello and Michelangelo. Donatello made two David, one was marble and one was bronze, but the ideas behind them are same. Donatello’s David stood still. He had successfully achieve his goal and killed Goliath, whose head lying at his feet. Michelangelo’s David was nude and had perfect athletic muscles and proportion, and fairly smooth flesh. His body was so perfect that made him immortal and divine. He had not yet embarked on the actual combat but would departure instantly. He stood still confidently. Michelangelo’s David was actually much more vivid than Donatello’s. Nevertheless, when compared to Bernini’s David, even the former seems lack the sense of motion. Bernini made his David a mortal. Bernini expressed a man in the middle of his ferocious action in an ultra realistic
...tellectus. However, while painting in the ratio he noticed some things were more beautiful to paint than others. Ratio is what caused him to not enter through the gates of heaven. He had not preserved his intellectus or true beauty of things. He had lost intellectus through realization of time, of time slowing. So, instead of letting time go he grabbed it which brought him to reason his paintings through the mind rather than the spirit.
As far as the human body is on the real and the anatomical features it fails to give an Idea of the human body in depth but an idea nonetheless. The painting in general is very proportional and in a way the people are proportional as a whole to the center; Jesus Christ. The main body part that seems to alwa...
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.
Bernini’s “David” is 5 foot, 7 inches tall and was made in the year 1623. It is from the Baroque period, a time of discovery, exploration and increased trade. Bernini’s “David” is a three-dimensional sculpture that gives the viewer the ability to relate the image with one’s body and not only in one’s mind. Bernini wanted to show the intensity and dramatic tension in the hero David as he prepares to cast the stone from the sling. In contrast to the intensity of Bernini’s David, Michelangelo’s “David” looks much more contemplative, statuesque and less “life-like” than Bernini’s. This marble sculpture, unlike Michelang...
This paper will discuss three specific instances: Le Sacrifice, Psappha, and Metastasis. The first principle that I will discuss is the Golden Section. The Golden Section can be found in art and architecture dating as far back as the Parthenon, as well as different places in nature, such as the nautilus shell. The Golden Section is essentially a proportion that is established by taking a single line and dividing that line into two separate sections of unequal lengths, one quite longer than the other.
Michelangelo’s David does not react with the surroundings but it stands alone with the little movements disguised behind it. The sculpture brings out David as a soldier preparing for war and not a person engaged in a battle (Miller, Vandome, & McBrewster, 2010). The hands are larger than normal and the arms are longer than his body. This is meant to illustrate the renaissance period. In contrast, the Bernini’s David has aspects of motion, showing that he was already engaged in the battle with Goliath. The idea of movement is enhanced by the loosely flowing robes. In addition, the sculpture demonstrates that unlike Michelangelo’s David that has longer hands, Bernini’s David has contracted muscles. The Michelangelo’s sculpture was created during Renascence period while the Bernini’s sculpture was done during the Baroque period.
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...
The David’s that we are going to compare are all within the Renaissance time period and by comparing them you can see the shifts in thought and viewpoint within that period. The three statues of David by Donatello, Verrocchio, and Michelangelo all are great depictions of this story while portraying values of the Italian Renaissance period. They have many things in common while also having their own
The aim of classical design has always been, according to Vitruvius’ De Architectura libri decem (De Architectura) known today as The Ten Books on Architecture, to proportion a harmonic structure. According to Marcus Vitruvius Pollio the theory of proportion is particularly important when it comes to designing a building, a passage in which his study relates human and architectural proportions he states:
To begin, the concept of unity follows the Aristotelian proposition that nothing can be added to or taken away from a perfect work of art. Next, proportion, or the harmony of the parts to the whole and to each other is, based the mathematical and geometric relationships discovered by the Ancient Greeks. Finally, clarity refers to the logical quality of design, as well as the luminosity of coloration. Therefore, St. Thomas explains that beauty is intimately tied to knowledge, and that we form our judgments according to what pleases us.
We claimed that Titian’s style is very significant to his artworks but something that is also as important is proportions, in the painting Adonis and Venus Titian didn’t over shadow one figure the other. Everything was in the right size and proportions. The objects like cupid and the dogs were very appealing size, the main focus was on the lovers, which Titian captured very thoroughly. He kept Venus and Adonis the same shape with similar body posture, twisted and agitated. Titian gave life different styles, proportions, and techniques he
...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.
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 ...
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.