The Golden Ratio
What is the "Golden Ratio" ?
In mathematics, two quantities are in golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The 2nd figure above illustrates the geometric relationship. Expressed algebraically, for quantites a and b with a > b > 0,
where the Greek letter phi ( or ) represents the golden ratio. Its value is :
The golden ratio has been claimed to have held a special fascination for at least 2,400 years, though without reliable evidence. According to Mario Livio :
Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way.
There are many other fascinating mathematical relationships and oddities in Phi series that can be explored in more depth, but for now let’s now take a step away from the purely mathematical and venture into nature, where Phi series manifest itself pervasively, but not universally. The positions and proportions of the key dimensions of many animals are based on Phi. Examples include the body sections of ants and other insects, the wing dimensions and location of eye-like spots on moths, the spirals of sea shells and the position of the dorsal fins on porpoises. Even the spirals of human DNA embody phi proportions.
History :
The golden ratio has been claimed to have held a special fascination for at least 2,400 years, though without reliable evidence. According to Mario Livio :
"Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics."
Applications and Beauty :
Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way.There are many other fascinating mathematical relationships and oddities in Phi series that can be explored in more depth, but for now let’s now take a step away from the purely mathematical and venture into nature, where Phi series manifest itself pervasively, but not universally. The positions and proportions of the key dimensions of many animals are based on Phi. Examples include the body sections of ants and other insects, the wing dimensions and location of eye-like spots on moths, the spirals of sea shells and the position of the dorsal fins on porpoises. Even the spirals of human DNA embody phi proportions.
Golden Ratio of the EARTH :
It has been claimed that the Golden Ratio of the Earth is in Mecca.
Phi to 15 places is 1.6180339887499. There are 180 degrees between the North Pole and the South Pole, so 180 divided by Phi is 111.2461179749810. As latitudes are expressed in degrees and distance from the Equator, we subtract 90 degrees and convert this to a latitude of 21 degrees, 14 minutes and 46.02 seconds, North or South.
The latitude of Mecca, according to Google Earth, is 21 degrees, 25 minutes and 38.56 seconds. This puts it only 10 minutes and 52.54 seconds north of the exact northern golden ratio latitude of the Earth. This is a variance of less about 1/10 of a percent, about 12 miles or 20 kilometers north of the exact golden ratio latitude point.
Composed By : Abdullah Riaz
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