Essays On Golden Ratio

Use of the Golden Ratio in Our World Essay

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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…show more content…

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 columns 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,

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What is the Golden Ratio

The golden ration can occur anywhere. The golden proportion is the ratio of the shorter length to the longer length which equals the ratio of the longer length to the sum of both lengths.

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.

The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called "phi".

The Golden Ratio is also known as the golden rectangle. The Golden Rectangle has the property that when a square is removed a smaller rectangle of the same shape remains, a smaller square can be removed and so on, resulting in a spiral pattern.

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 1.618Ð'...Ð'...

Golden Ration = Length = 1.6


The golden rectangle has been discovered and used since ancient times. Our human eye perceives the golden rectangle as a beautiful geometric form. The symbol for the Golden Ratio is the Greek letter Phi.

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.

The Renaissance used the Golden Mean and Phi in their sculptures and paintings to achieve vast amounts balance and beauty.

The Golden Ratio in Architecture and Art

Throughout the centuries, artists have used the golden ratio in their own creations. An example is "post" by Picasso. When using a golden mean gauge you can see that the lines are spaced to the Golden Proportion.

The Golden Ratio also appears in the Parthenon in Athens. It was built about 440 B.C.; it forms a perfect Golden Rectangle. The exterior


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