Since ancient times, mankind had been always looking for beauty and proportion in all things. In every era, someone had dedicated his life to find the most excellent method to express Aesthetic through art (Architecture, Book Design, Painting, Music, Design, etc). One of the two great treasures of Geometric is the division of a line into extreme and mean ratio. Whit this formula the Greeks answered to the question: how can we divide a line in two sections to have the most appeal balance? The Greeks claimed that the most visually pleasing division has the property that the ratio of the length of the entire line segment to the length of the long piece, and they expressed with this formula: L/1=L+1/L. It seems kind of confusing, but with practice it will be easier to appreciate it on art expressions. This formula helped to find what we know today as the Golden Ratio or as sometimes it called the divine proportion. The Golden Ratio is represented by a Greek symbol and it is the number 1.61803. For years they introduce this Golden Section to different compositions, but later on trying to created better compositions, they discovered another great system to express beauty The Golden Rectangle. The Golden rectangle is a perfect proportionate shape, which helps to create balanced and beautiful compositions. A Golden Rectangle can be any size, but it has to maintain this proportions: ratio=8/5. Since then, many artists had been using this on their masterpieces. Actually, nowadays The Golden Rectangle is used on note cards, cereal boxes, and in general in media publicity. We can form a Golden Rectangle by using the formula, which means that its longer side is radio times as long as its short side. Some people had done some investigatio... ... middle of paper ... ...) we see that 8 times 8+5 that is equal to 8 times 13, and we divide this number 13/8 we got this number 1.625 and we go on the creations of more shapes we will closer to this number 1.608033 that we known as the Golden Section. There are several examples on nature about this perfect, beautiful and proportionate creation. Some of them are the sunflowers, the Pinwheel Galaxy, the Aloe plant, some type of flowers, some insects, the Nautilus as I mentioned before, and so many other examples. As a conclusion, if we are looking for a living prove of perfection through balanced proportions, we just have to see around us and appreciated the excellence on nature. Mathematics are used to created beauty as well, and if we applied this sections in our daily life we will able to create beautiful compositions, but overall we will able to appreciated beauty through Mathematics.
The ratio is explained simply like this. According to the Adonis Golden Ratio review the distance between your head and navel is about 1:1.618 of the distance from your head down to your fingertips. As mentioned earlier this is the same formula that artist like Leonardo da Vinci used with another equally gifted artist/architect. This is the measurements that captures women attention whether they like it or not. There is something pleasing about looking at the male physique that looks nearly flawless and
Thousands of artists emerge from their mindless slumber to paint rosy cheeks and draw cat inspired winged eyes. These artists sketch over-plucked eyebrows and draw arches to a create strange self-described works of art, that they believe to be aesthetically pleasing. If these artists see a glimpse of imperfection, their masterpiece is ruined and their canvas has to be wiped clean. The artist is seeking the approval and acceptance from their well-known art critics, so this masterpiece has to be their finest work of art.
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.
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.
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...
Areas of the following shapes were investigated: square, rectangle, kite, parallelogram, equilateral triangle, scalene triangle, isosceles triangle, right-angled triangle, rhombus, pentagon, hexagon, heptagon and octagon. Results The results of the analysis are shown in Table 1 and Fig 1. Table 1 showing the areas for the different shapes formed by using the
I am going to begin by investigating a square with a side length of 10
world and this value of form and thought can be seen throughout many of the works of art.
Then in Euclid II, 7, it goes farther to explain that “if a straight line be cut at random, the square on the whole and that on one of the segments both together, are equal to twice the rectangle contained by the whole and said segm...
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.
During the ancient times in Greece, Plato was the first human to document and criticize the existence of art and artists. He mentioned that human art was always in a form of a representation of something else. In one of Plato’s famous works, he demonstrates the idea of art is like an “imitation of nature” (Blocker 3). In other words, the purpose of art was to represent nature and nothing else. Art was not created for the sake of its own self nor was it created to appreciate its own beauty by any means. Instead, art, usually in forms of writings, paintings, or sculptures, was created to only to represent nature, Gods, emperors, families, or other important individuals. Furthermore, Plato had a very critical view towards the existence art in our society because art makes us more emotional, and our emotions lead to many errors about life. He believed it is our rational thinking, not our emotions or senses, which helps us und...
It is constructed by taking an equilateral triangle, and after many iterations of adding smaller triangles to increasingly smaller sizes, resulting in a "snowflake" pattern, sometimes called the von Koch snowflake. The theoretical result of multiple iterations is the creation of a finite area with an infinite perimeter, meaning the dimension is incomprehensible. Fractals, before that word was coined, were simply considered above mathematical understanding, until experiments were done in the 1970's by Benoit Mandelbrot, the "father of fractal geometry". Mandelbrot developed a method that treated fractals as a part of standard Euclidean geometry, with the dimension of a fractal being an exponent. Fractals pack an infinity into "a grain of sand".
The Golden Rectangle is a unique and important shape in mathematics. The Golden Rectangle appears in nature, music, and is often used in art and architecture. Some thing special about the golden rectangle is that the length to the width equals approximately 1.618……
...its relation to the Golden Angle, which appears in the primordia of plants in order to give the maximum number of primordia for plants. I like to think of an idea in the book, ?Life?s Other Secret,? which says that it?s not just Fibonacci Numbers that matter; it?s also the matter in which they arise (Stewart).
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 ...