The Golden Ratio Essay

1026 words - 4 pages

The Golden Ratio

Certain pictures, objects, and animals appeal to the human mind more than others. Proportions and images of symmetry often contribute to our fascination with them. Often, when examined carefully, you may find a common “coincidence” between man made objects and those found naturally in nature. This fluke, however, may be used to ascertain various mathematical relationships between these objects. This paper will introduce the golden ratio and weigh its significance on math, art, and nature.

1.6180339887…. has been given many names varying from the “golden ratio” first coined by the Greeks, to the “golden rectangle” and “golden section”, “phi” named after Phidias a renowned Greek sculptor, as well as the “divine proportion” conceived by Leonardo da Vinci. (Blacker, The Golden Ratio) Simply put, the golden ratio is the length to width of rectangles used in art and nature. This ratio is considered to be the most agreeable arrangement, mathematically and artistically, to the eye.

Perhaps the first to use the golden ratio were the Egyptians. Many (if not all) of the pyramids were made with the golden ratio kept solely in mind… as if they were made only using the ratio. Later, the Greeks began using it in their architecture as well as their sculptures. Phidias and others popularized the golden ratio by basing their achievements on it. The Parthenon, specifically, as well as several other buildings and sculptures were the subject of which the ratio has left its mark.

The Greeks and the Egyptians were by far not the only people to have been affected by the number. Famous painters and mathematicians have also recognized the ratio’s significance.

Perhaps the most famous and blatant use of the golden ratio has come in the works presented by Leonardo da Vinci. Born in 1452 Leonardo da Vinci was born quite insignificant but rose to fame through his incredible array of skills.

The definitive polymath, he had almost too many gifts, including superlative male beauty, a splendid singing voice, magnificent physique, mathematical excellence, scientific daring… (Beckett, 117)

He studied at various places including Milan and Florence and the Vatican. It is in these cities that he became famous. He masterfully uses the golden ratio in the Mona Lisa framing her head as well as the rest of her body parts in exact proportion to the golden rectangle. Furthermore, he goes on in such works as the Vitruvian Man and Virgin and Child with St. Anne to incorporate the golden rectangle into everything he possibly can. He was by no means enthralled in art.

Instead, his great passions were mathematics and the natural world, and he compiled volumes of detailed drawings and notes on anatomy, botany, geology, meteorology, architectural design, and mechanics. (Stokstad, 693)

Toward the end of his life math, particularly the golden ratio, began to dominate everything he created. Leonardo da Vinci died in 1519.


Find Another Essay On The Golden Ratio


2427 words - 10 pages proportions. The rule of Golden Proportion considers only the widths of teeth. However, esthetic perception is related directly to width-to-length ratio of teeth. Later, the concept of Recurring Esthetic Dental Proportion was introduced. Ward in 2000 proposed RED proportion based on different lengths of the maxillary teeth.3,4,5 The proportions were given for very tall, tall, normal, short and very short teeth. This theorem states that as we move

A summary of the work and discoveries made by Pythagoras and the Pythagorians.

566 words - 2 pages ) Between one and 10,000 there are only four of these; 6, 28, 496 and 8128. The Pythagoreans compared this to humans: very few are perfect, good and beautiful. But imperfection in numbers is common, just like evil and ugliness in people.The Golden Ratioa/b= 1.618If you divide the longest side of a square with the short side of the square and get 1.618 the square has a Golden Ratio. Here is an example:If you divide 3.2 cm with 2.0 cm you get 1.618


1252 words - 5 pages aspect of the golden ratio and the rule of thirds had to be added to this photo. Therefore, I searched it up in Google, golden ratio template and learned how to do some golden ratio. However, my picture was not totally balanced overall, therefore, I cropped some of the parts in the picture using grids since the template of the rule of third is made by dividing the picture in to vertical and horizontal lines. I used the aspect of golden spiral by

Fibonacci Numbers

606 words - 2 pages value, which theGreeks called the golden ratio and has the value 1.61803. It has some interestingproperties, for instance, to square it, you just add 1. To take its reciprocal, you justsubtract 1. This means all its powers are just whole multiples of itself plus anotherwhole integer (and guess what these whole integers are? Yes! The Fibonaccinumbers again!) Fibonacci numbers are a big factor in Math, The Golden Ratio,The Pascal Triangle, the production of many species, plants, and much muchmore.

Math History: The Life and Numbers of Fibonacci

640 words - 3 pages Golden Ratio and Fibonacci Numbers by Richard A. Dunlap on page 35, the rabbit breeding problem is as follows:A pair of adult rabbits produces a pair of baby rabbits once each month. Each pair of baby rabbits requires one month to grow to be adults and subsequently produces one pair of baby rabbits each month thereafter. Determine the number of pairs of adult and baby rabbits after some number of months. It is also assumed that rabbits are

Math and Music: An Introduction and Mathematical Analysis

1383 words - 6 pages . It can be derived from the monochord, and consistent with Pythagorean doctrine, all of its intervals can be expressed as ratios of integers. The Pythagorean could still appreciate in beauty inherent in the discovery that ratios of whole numbers produced consonant intervals. Golden Ratio in Mozart’s Works Mozart often composes his sonatas in two parts. The first piece that gives an introduction about the musical theme is called the

Scholars Being Justified in Using the Term Golden Age to Describe the Economic History of Western Europe During 1950-1973

2059 words - 8 pages an explanation of the ‘Golden Age’ through an approach known as “growth accounting”. Observing a huge increase in the ratio of investment to GDP and incorporating technical progress, Maddison argued that investment itself was the main cause of Europe’s performance in productivity growth. For Maddison the implementation of new favourable policy and the increase in technology transfer led to the growth in total factor

Failure Analysis Report on the Tacoma Narrows Bridge

718 words - 3 pages bridge took to damp them out was of concern to the engineers involved. The length of time Tacoma Narrows Bridge needed to damp out its oscillations was unlike other similarly built suspension bridges, namely the Golden Gate Bridge, whose oscillations were quickly damped due to its larger width-to-span ratio. (need connecting sentence)Just before the total failure of the bridge the oscillations changed from their standard vertical and horizontal to a

Management Accounting: Golden Bakeries LTD - CVP Analysis.

921 words - 4 pages reason is variable cost ratio is 13.3% more higher than bread rolls. It's proposed that Golden Bakeries decreases the cost of material and labour, improve the management and efficiency of work at the same time. Donuts contributes only 7.6% percentage in overall profit of the period of accounting.C. Fudge CakesThe contribution percentage provided from the sales of Fudge is only 16.7% same like Bread rolls. The contribution margin is 27%, around 10

music and math

3113 words - 12 pages …). However, their most important feature in this context is that the sequence of Fibonacci ratios (that is the ratio of a Fibonacci number with its bigger adjacent) converges to a constant limit, called the golden ratio, golden proportion or golden section (0.61803398…). More common is the geometric interpretation of the golden section: A division of a line into two unequal parts is called golden if the relation of the length of the

The Influence of Humanism in the Architecture of Classical Greece and Rome

965 words - 4 pages the goddess Athena as the city's patron divinity (“Religious Life”). In addition, the Parthenon’s east pediment describes the birth of Athena, and the west pediment describes the story of when Athena defeats Poseidon for control over Athens. Furthermore, the Parthenon was turned into a Christian church in the 5th Century AD. The Parthenon was designed to be aesthetically perfect to the human eye. The golden ratio is when the

Similar Essays

The Golden Ratio Essay

1016 words - 4 pages The golden ratio is approximately 1.6. The mysteriously aesthetically pleasing ratio is the relation "a+b is to a as a is to b" or a+b/b=a/b=φ. It is denoted as the Greek letter φ or Φ (lower case, upper case respectively, upper case most often used as reciprocal). The letter is pronounced "phi". The golden ratio is found prominently in art, nature, and architecture. Throughout the centuries countless mathematicians have spent

The Golden Rectangle And Ratio Essay

1881 words - 8 pages The Golden Ratio The Golden Rectangle and Ratio The Golden Rectangle and Golden Ratio have always existed in the physical universe. Nobody knows exactly when it was first discovered and applied to mankind. Many mathematicians assume that the Golden Rectangle has been discovered and rediscovered multiple times throughout history. This would explain why it is called many different names such as the Golden Mean, divine proportion, or the

Assignment Regarding The Fibonacci Sequence And The Golden Ratio Maths Assignemnt

4102 words - 16 pages the Hexagonal Numbers. There is many patters found in this row, and this is only looking at one row in the triangle.Picture care of golden ratio can also be achieved using Pascal's triangle but its more using the Fibonacci sequence, although as the Fibonacci sequence is in Pascal's triangle we can say it is there. But if in Figure 1.1 you divide each number by the previous in the end you get

Fibonacci Numbers Essay

2277 words - 10 pages , the square root of 21 is 441 and the square root of 8 is 64. When you subtract them, the difference is 377, 377 is a Fibonacci number. Fibonacci numbers are unique in various ways. According to the Merriam-Webster dictionary “The golden section is a proportion in which the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller.” 1.61803398874989484820... is the ratio. This ratio is known as the golden