Egyptians used the Golden Ratio for their pyramids and the layout of the three great pyramids of Giza use the curve of the Golden Ratio that is predominant in a nautilus shell. The sunflower positions its seeds in a Golden Ratio spiral because it is the most effective manner of having as many seeds in a given amount of space possible and allowing them to remain un-crowded within that space.īelow is a flower that one can still see a spiral pattern emerge from the middle buds.Īncient Greeks were not the only ones who understood the Golden Ratio. Why this ratio of 1.618? This ratio provides the flower petals and leaves with maximum exposure to sunlight and allows rain drops to flow down to the root in the most effective manner. Flower petals and pinecones are two examples of spiral designs that use the Golden Ratio. The Golden Mean or Phi and the Golden Ratio abound in nature and perhaps humanity has been genetically programmed to recognize the ratio as being pleasing. Each succeeding number after 1 is equal to the sum of the two preceding numbers.Īdd enough golden rectangles arranged a certain way and soon you will have the golden curve that spirals around like a nautilus shell.

Technically, the golden rectangle is composed of two parts that follow the Fibonacci sequence.ġ,1, 2, 3, 5, 8, 13, 21, 34 etc. It can be seen as another example of the rule of thirds as the rectangle can be made up of three equally sized smaller rectangles. This rectangle is comprised of a square and one-half of another square that is the same dimension together, as seen below. The more traditional physical shape of the Golden Ratio is the golden rectangle. A most intriguing and apparently an excellent sounding speaker. The Bowers and Wilkins speaker company of Britain, better known as B&W, designed a reference speaker with the nautilus design and called it…the Nautilus. One of the most interesting graphic forms of the Golden Ratio is the nautilus shell and the way the shell starts from a central origin and then spirals outward around itself until it reaches the horn or opening of the shell where the cephalopod's head is located. The shape of the Golden Ratio in physical form is supposed to be considered very esthetically pleasing to humans. Leonardo da Vinci being the most prominent Renaissance artist known to have used the Golden Ratio for great works such as the Mona Lisa.

During the Renaissance when European artists rediscovered the styles of the ancient world, the Golden Ratio was utilized for their sculptures and paintings. The Golden Ratio has purportedly been a profound influence since ancient times with Greeks utilizing the Golden Ratio in their buildings such as the Parthenon at the Temple of Athena on the Acropolis. Mathematicians have even come up with a formula for the human decision-making process, better known as Game Theory or the Zero Sum Gain.

Mathematicians seem to love to apply numbers to what seemingly could or should not have numbers applied to them but still there are many geniuses out there seeking a single mathematical formula that would explain the nature of the universe and of life itself. Loosely related to the rule of thirds is the Golden Ratio also referenced to the Golden Rectangle.

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