The Golden Ratio Essay, Research Paper
The Golden Ratio and Our World
Leonardo of Pisa, better known as Fibonacci, was born in Pisa, Italy, about 1175 AD. He was known as the greatest mathematician of the middle ages. Completed in 1202, Fibonacci wrote a book titled Liber abaci on how to do arithmetic in the decimal system. Although it was Fibonacci himself that discovered the sequence of numbers, it was French mathematician, Edouard Lucas who gave the actual name of “Fibonacci numbers” to the series of numbers that was first mentioned by Fibonacci in his book. Since this discovery, it has been shown that Fibonacci numbers can be seen in a variety of things today.
He began the sequence with 0,1,… and then calculated each successive number from the sum of the previous two. This sequence of numbers is called the Fibonacci Sequence. The Fibonacci numbers are interesting in that they occur throughout both nature and art. Especially of interest is what occurs when we look at the ratios of successive numbers. The Fibonacci numbers play a significant role in nature and in art and architecture. When you construct a set of rectangles using the sequence (1, 1, 2, 3, 5, 8, 13, 21,), a design found in nature is revealed:
Next, when you construct in each square an arc of a circle with a radius the size of the edge of each respective square (a quarter circle), the organic design, which can be found in a snail shell can be seen:
Throughout history the length to width ratio for rectangles was one to 1.61803 39887 49894 84820. This ratio has always been considered most pleasing to the eye. This ratio was named the golden ratio by the Greeks. In the world of mathematics, the numeric value is called “phi”, named for the Greek sculptor Phidias. The space between the collumns form golden rectangles. There are golden rectangles throughout this structure which is found in Athens, Greece.
He sculpted many things including the bands of sculpture that run above the columns of the Parthenon. Phidias widely used the golden ratio in his works of sculpture. The exterior dimensions of the Parthenon in Athens, built in about 440BC, form a perfect golden rectangle.
Many artists who lived after Phidias have used this proportion. Piet Mondrian and Leonardo da Vinci both thought that art should manifest itself in continuous
movement and beauty. Therefore, they both expressed movement by incorporating the golden rectangle into their paintings. The golden ratio expresses movement because it keeps on spiraling to infinity. They showed beauty in their paintings by using the golden ratio because it is pleasing to the eye. To express the Fibonacci Sequence in art one must pay close attention to beauty, proportions, and continuous rhythm.
Leonardo Da Vinci dubbed this proportion the “divine proportion.” If you draw a rectangle around Mona Lisa’s face, you would find that the rectangle is in the golden proportion. He did an entire exploration of the human body and the ratios of the lengths of various body parts.
A modern day artist that used the golden ratio in a numerous amount of paintings was Mondrian. Piet Mondrian avoided any suggestion of reproducing the material world. Instead using horizontal and vertical black lines that outline blocks of pure white, red, blue or yellow, he expressed his conception of ultimate harmony and equilibrium. His style, and its underlying artistic principles, he called neoplasticism. Here is an example of one of his angular paintings which employ the proportion:
Composition with Gray and Light Brown
by Piet Mondrian
1918 (170 Kb);
Oil on canvas, 80.2 x 49.9 cm;
Museum of Fine Arts, Houston, Texas
Другие работы по теме:
Golden Age Of Athens Essay Research Paper
Introduction EssayThe era of classic Greece from 460 to 429 b.c.e. was known as the Golden Age because during those years Athens made great achievements to the world. The 5th century BCE was a period of great development in Athens. The development of so many cultural achievements within Athens has led scholars to deem this period a “Golden Age.”The 5th century and the Athenian Empire gave birth to an amazing amount of accomplishments.
My Buddy Essay Research Paper My Buddy
My Buddy Essay, Research Paper My Buddy is about a boy who has muscular dystrophy. The boy is in a wheelchair and he relies on others to help him because his muscles are too weak. The boy gets a service dog named Buddy. He is a golden retriever, who assists the boy with everyday tasks. Buddy and the boy go through training with one another.
The SoCalled Golden Age Of Women Essay
, Research Paper The occurrence of events during a specific period of time always introduces different mentalities and ideas to everybody in the world. Such is the case with
Long Term Analysis Essay Research Paper Analysis
Long Term Analysis Essay, Research Paper Analysis by a Long Term Creditor The interest a long term creditor is currently receiving is 5.6%. A long term creditor could receive as much as 22.7% working somewhere else in the same industry. So, currently the industrial average is giving 17.1% more interest than workingat Cameco Corporation, which is quite a big difference.
Medea 2 Essay Research Paper In the
Medea 2 Essay, Research Paper In the play Medea there were two main characters Medea and Jason. We have seen these characters before in the story of The Golden Fleece. Medea met Jason on his quest for the Golden Fleece. They immediately fell in deep passionate love for each other. Although Medea had a little help because she was under a love spell put on her by cupid.
Density Of Urine Essay Research Paper The
Density Of Urine Essay, Research Paper The term ‘density’ refers to the proportion of an object’s mass to it’s volume (Grasse, 1996). The ratio between the density of a substance and the density of water is called specific gravity and is used in many diagnostic tests. ONe example is the specific gravity of urine which is normally determined as part of a laboratory evaluation of the health of an individual.
Creative Poem Essay Research Paper Hope you
Creative Poem Essay, Research Paper Hope you are enjoying the Day! To have a friend, you must be a friend, Starting with yourself. The greatest hunger a person has is to be needed.
Fibonacci Essay Research Paper Fibonaccia Introduction1 About
Fibonacci Essay, Research Paper Fibonacci(a) Introduction(1) About Fibonacci(1) Time period (Hog 1)(2) Fibonacci s Life (Hog 1), (Vaj 9)(3) The Liber Abaci. (2) The Fibonacci Sequence(1) When discovered (Vaj 7)(2) Where it appears (Vaj 9)(3) The Golden Ratio(1) When discovered(2) Where it appears(4) Thesis: The Fibonacci Sequence and The Golden Ratio are very much a part of one another, and these two phenomena have many applications in math and nature. (b) The Simple explanations(1) How we arrive at the Fibonacci Sequence(1) Explained in English(2) Formula(2) The Simplest Properties of the Fibonacci Numbers(1) u1+u2+…+un=un+2-1 (Vor 6)(2) The sum of Fodd: u1+u3+u5+…+u2n-1=u2n (Vor 7)(3) Sum of Feven: u2+u4+…+u2n=u2n+1-1 (Vor 7)(4) u12+u22+…+un2=unun+1(Vor 8)(3) How we arrive at the Golden Ratio(1) Explanation of it. (1) Explanation of Golden Rectangle(2) Formula to get it. – Solve for
The Golden Age Essay Research Paper The
The Golden Age Essay, Research Paper The Myth of the Golden Age In the essay “The Myth of the Golden Age” by Mary Beth Norton, Mary did not agree with historians that is was a “Golden Age” for women during the colonial period. She feels that women’s lives outside the home were severely limited. Mary felt women never achieved a status later to be lost.
Rock N Roll Essay Research Paper From
Rock N Roll Essay, Research Paper From jazz and boogie of the thirties moved popular music away from the light entertainment of the theater toward a more exiting and dance oriented style that made the swing era a golden age. Do to jazz moving into rhythm and blues black people were recognized for talents in music and dance.
Crucible Lying Essay Research Paper Notes for
Crucible Lying Essay, Research Paper Notes for an essay on human weaknesses that are prominent in the Crucible Lying (pg. 10 – Abigail Williams) Abigail lied to Parris when he asked if she had
Glass Ceiling Summary Essay Research Paper Utilitarianism
Glass Ceiling Summary Essay, Research Paper Utilitarianism favors unequal treatment in the work place.CONTROLLING IDEA: Big corporations should be forced into applying affirmative action to equal out the male/female ratio in management positions.
Muhammad Ali Essay Research Paper The name
Muhammad Ali Essay, Research Paper The name Muhammad Ali needs no introduction in the sports industry. This man is a living legend. Ali has accomplished my achievements during an era when African-Americas weren?t allowed any opportunities.
Barnes Vs Amazon Essay Research Paper Amazon
Barnes Vs. Amazon Essay, Research Paper Amazon and Barnes and Noble In the decision of investing in Amazon or Barnes and Noble, I recommend neither. Looking at the present state of both companies, neither displays good, strong expectations of profits. Instead, I see both companies with low projected earnings growth ratios and negative cash flow.
My Golden Age Essay Research Paper Many
My Golden Age Essay, Research Paper Many people have their own Golden Ages. It is like a dream that a person would like to live out. Many of these dreams tend to be similar to a utopia, or a perfect world. Due to the fact that their Golden Age is a perfect world, most of these dreams are a little bit on the unrealistic side.
The Golden Marmoset Essay Research Paper Golden
The Golden Marmoset Essay, Research Paper Golden marmosets, or Leontopithecus chrysomelas, have a mane derived from long hairs on the top of the head, cheeks and throat. The golden marmoset is predominantly black with golden to reddish-orange on the front of the mane, the lower half of the front paws and part of the tail.
End Of Time Essay Research Paper End
End Of Time Essay, Research Paper End of Time I cannot find a way around, Searching high but falling low, Fighting where the soul won’t go. In the world, a corrupted ghost,
Bless Me Ultima Essay Research Paper Talfud
Bless Me Ultima Essay, Research Paper Talfud once said that, Men see in their dreams only that what is suggested by their own thought. In Bless Me Ultima, the passage after Narciso s death is crucial in understanding that Antonio processes his conflicts in his dreams. This passage is key for the understanding that Antonio s dreams are his way of processing his conflict between the Catholic God and the Golden Carp.
My Golden Moment Essay Research Paper A
My Golden Moment Essay, Research Paper A Golden Moment June 26, 1999 was a significant ?Golden Moment? in my life. The overwhelming feeling of freedom, responsibility, fear, and excitement embellished my body with it?s intoxicating smoke. Am I
Dear Golden One love Letter Based On
Anthem) Essay, Research Paper Dear Golden One,IT IS NOT A SIN TO WRITE THIS! I’m very tired of having to hide my feelings for you. My heart is about to explode of the passion that is burning its inside when I can’t have you. What is wrong with loving each other? Why can’t I just hold you and show you how much I care about you? My dear love, you have always being my inspiration at everything I do.
Adam And Eve Essay Research Paper In
Adam And Eve Essay, Research Paper In the ?Book of Genesis?, an ancient Hebrew story from the King James Bible, we are given the account of Adam and Eve. Eve is led up the path of temptation and forced to make a
Sea Eagles Essay Research Paper The sea
Sea Eagles Essay, Research Paper The sea eagle, which is also called an erne, is not closely or at all related to the golden eagles but is somewhat realted to certain kinds of vultures. The sea eagal has unfethered lower legs, and a bright yellow bill. Which is a lot longer and heavier than the gray bill of the golden eagals.
1984 Essay Research Paper Ever looked outside
1984 Essay, Research Paper Ever looked outside the window and seen a dove? A white dove in particular? The white dove in the dictionary is defined as a small wild pegion, however, the symbolic
Common Eileen Essay Research Paper Wordsworth begins
Common Eileen Essay, Research Paper Wordsworth begins his extended metaphor in the third line of the poem, with his speaker saying, ?I saw a crowd, / a host, of golden daffodils? that were ?fluttering and dancing in the breeze.? (line 6). The speaker is attributing to these daffodils human qualities: their forming a crowd, and their dancing.
Colonial Women Essay Research Paper Women during
Colonial Women Essay, Research Paper Women during the Colonial Period Carr and Walsh believe that the colonial age was indeed a ?Golden Age? for women in America. Although the re was not much evidence that women were powerful when it came to handling the estate of her husband, especially after his death. After the death of her husband, the woman is given one third of his land.
My Dog Skippy Essay Research Paper When
My Dog Skippy Essay, Research Paper When I was little I loved animals. Although most children have pets, I could not convince my parents into allowing me to have one until my pre teens. I could not have been happier the day my family went to the pound and I picked out my dog Skippy. Skippy loved to run and he was loyal to me and I will never forget the day I lost him.