<b>The Golden Ratio</b>

The Golden Ratio

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Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. One of the mysteries is F (= 1.6180339887… ), this curious mathematical relationship, widely known as “The golden ratio”, was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. It is believed that the creators of the Pyramids and Parthenon employed it.

Ancient Greek mathematicians first studied the golden ratio because of its frequent appearance in geometry. The division of a line into the golden section is important in the geometry of regular pentagrams and pentagons. Euclid’s Elements provides the first known written definition of the golden ratio.

Evidence exists that the ratio may have been known to the ancient Egyptians (1650 BC). Egyptians referred it as “sacred ratio”. The ratio of the altitude of a face of the Great Pyramid at Gizeh to half the length of the base is 1.618.

Through the ages other names have been attached to this wonderful ratio including golden ratio, golden mean, golden number and divine proportion.

Another starting feature of the golden ratio is that we produce its square by simply adding the number 1; i.e. F2 = F + 1.

Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets. It is used in trading algorithms, applications and strategies.

In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals. Several researchers have proposed connections between the golden ratio and DNA.

The golden ratio is an irrational mathematical constant, the value of which is approximately 1.61803398874989. It is denoted by F.

The golden ratio is one of the most exotic mathematical constants that has attracted attention of mathematicians for many centuries; artists, architects, biologists, chemists, financial analysts also found it equally startling.

Many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. The golden ratio is aso used in the analysis of financial markets.

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