The Golden Ratio
“Without mathematics there is no art.” – Plato. Many people wonder why something looks more attractive than other things. There are many variables for this like: color matching, placement, shape, size, and symmetry. There is one answer for that question, it is called, the golden ratio, or phi. Phi is the twenty-first letter in the Greek alphabet, but in math it is a ratio. This ratio can be applied in modern day architecture, art, and logos for spacing, size, and looks. All people need to do is follow the ratio rules.
“The golden ratio was studied in Greece by the mathemation Phidias” (Phi). He later applied it to the sculptures for the Parthenon. A European philosopher named Plato also studied it; he believed that the golden ratio can be the binding of all mathematical relationships, and the physics of the cosmos. It was first noted in the European countries for study, people believe the Egyptians used it first. Buildings from the past and present use this ratio like: CN tower, and the Notre Dame. It may seem that the golden ratio can only be used in architecture, but it can also be seen in nature, and in art.
Phi is an irrational number, this means that it can go on forever. When people look up what Phi is equivalent to 1.618; though it does not exactly equal that because it’s ever lasting. The most irrational famous number is Pi or 1.141. When humans try and calculate phi it will take a very long time depending what number you pick. To calculate it people pick a number, then divide by one, finally add one to that new number. This process can take awhile depending on how high the number is. Now the Fibonacci number sequence is different. Fibonacci is a sequence of number just like counting one to ten, but th...
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...o the distance in between the two circles. With these circles you divide the diameter of the two circles “a/b.” Apple is one of the few huge companies in the world that does not contain the company name in their logo; its because it is designed with the golden ratio and the Fibonacci numbers. You can remember this logo without studying it because of its design. This can possibly change the designs of logo for all companies so people will remember them.
The golden ratio can easily be applied and use frequently in today’s society. With it perfecting things one by one. Only things can be perfect with the missing variables like: shape, size, color, and placement. More and more studies can be added on to this ratio because of the fascination of perfection though the human brain. “The good, of course, is always beautiful, and the beautiful never lacks proportion.”- Plato.
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
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 contemporary world is full of marvels. Technological advances have enabled mankind to fly in the heavens, instantaneously communicate with distant relatives thousands of miles away, construct buildings that are able to withstand many natural disasters, cure deadly diseases, and even travel to and study areas beyond the confines of planet Earth. While there are many factors that contributed to man’s ability to overcome what many once thought were impossible feats, it is the study of engineering that has enabled one to study the elements and leverage all that they have to offer. Mathematics lies at the heart of all science, including engineering. Without progressions in mathematical concepts, engineering principles and applications would not have advanced as quickly as they have throughout history.
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 ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as a number that can be found when a line or shape is divided into two parts so that the longer part divided by the smaller part is also equal to the whole length or shape divided by the longer part. The Ancient Greeks and Romans incorporated it and other mathematical relationships, such as the triangle with a 3:4:5 ratio, into the design of monuments including the Great Pyramid, the Colosseum, and the Parthenon. Artists who have been inspired by mathematics and studied mathematics include the Greek sculptor Polykleitos, who created a series of mathematical proportions for carving the ‘perfect’ nude male figurine. Renaissance painters such as Piero della Francesca an...
It is amazing to see how mathematics has such an influence on the world and the evidence it creates. The world is affected by numbers and mathematics all the time and this mysterious number known as the golden number has proven to be the center of everything.
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.
The recursive sequence of numbers that bear his name is a discovery for which Fibonacci is popularly known. While it brought him little recognition during the course of his life, is was nearly 100 years later when the majority of the mathematicians recognized and appreciated his invention. This fascinating and unique study of recursive numbers possess all sorts of intriguing properties that can be discovered by applying different mathematical procedures to a set of numbers in a given sequence. The recursive / Fibonacci numbers are present in everyday life and they are manifested in the everyday life in which we live. The formed patterns perplex and astonish the minds in real world perspectives. The recursive sequences are beautiful to study and much of their beauty falls in nature. They highlight the mathematical complexity and the incredible order of the world that we live in and this gives a clear view of the algorithm that God used to create some of these organisms and plants. Such patterns seem not have been evolved by accident but rather, they seem to have evolved by the work of God who created both heaven and
It is well known that in the past, Renaissance artists received their training in an atmosphere of artists and mathematicians studying and learning together (Emmer 2). People also suggest that the art of the future will depend on new technologies, computer graphics in particular (Emmer 1). There are many mathematical advantages to using computer graphics. They can help to visualize phenomena and to understand how to solve new problems (Emmer 2). “The use of ‘visual computers’ gives rise to new challenges for mathematicians. At the same time, computer graphics might in the future be the unifying language between art and science” (Emmer 3).
‘Nature abounds with example of mathematical concepts’ (Pappas, 2011, .107). It is interesting how much we see this now we know, regarding the Fibonacci Sequence, which is number pattern where the first number added to itself creates a new number, then adding that previous number to the new number and so on. You will notice how in nature this sequence always adds up to a Fibonacci number, but alas this is no coincidence it is a way in which plants can pack in the most seeds in a small space creating the most efficient way to receive sunlight and catches the most
Fibonacci Numbers originated from India hundreds of years ago. Though Fibonacci Numbers came from India, Leonardo of Pisa, better known as Fibonacci, made it known to the world. Leonardo came from a wealthy Italian family and traveled to North America to join his father. He was educated by the Moors and sent on business trips. “After returning to Pisa around 1200, Leonardo wrote his most famous literature, Liber Abaci” (Pearson). Leonardo featured a rabbit question in the book. The question was asked in a mathematical competition, he appeared in when he was young. Leonardo Fibonacci used the Fibonacci Numbers to solve it. Fibonacci Numbers is now used throughout our society.
...ld be one way to introduce an additional idea: that beauty is inherent in mathematics.
The Fibonacci Series was discovered around 1200 A.D. Leonardo Fibonacci discovered the unusual properties of the numeric series, that’s how it was named. It is not proven that Fibonacci even noticed the connection between the Golden Ratio meaning and Phi.
...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).
Fibonacci sequence has been a big factor in many patterns of things in nature. One has found that the fractions u/v representing the screw-like arrangement of leaves quite often are members of the fibonacci sequence. On many plants, the number of petals is a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals. Fibonacci nmbers are also used with animals. The first problem Fibonacci had wehn using the Fibonacci numbers was trying to figure out was how fast rabbits could breed in ideal circumstances. Using the sequence he was ale to approximate the answer.