Posted on July 07, 2016 by Mary Hood | 0 Comments
From hurricanes to ancient architecture to the center of sunflowers, examples of the Golden Ratio are all around us.
The Golden Ratio.
Live Science defines the Golden Ratio (also called the Golden Mean or Divine Proportion) as “a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part. It is often symbolized using phi, after the 21st letter of the Greek alphabet.” As with pi, the golden ratio is a number whose decimal points go on ad infinitum. 1.61803398875… is just the beginning. Phi is usually rounded off to 1.618. The equation is expressed as a/b = (a+b)/a = 1.618…
The Golden Ratio has been discovered and rediscovered by mathematicians throughout ancient history and across cultures. The ratio may be seen in the proportions of great ancient architecture including the Great Pyramid of Giza and the Parthenon. Plato (428 - 347 BCE) described the ratio as the most “universally binding mathematical equation.”
A full-scale recreation of the Parthenon in Nashville, TN.
The Golden Ratio is closely related to the Fibonacci Sequence discovered by Leonardo Fibonacci in 1202. Fibonacci Sequence is a sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… The expression is written as xn = xn-1 + xn-2. The Ratio of two successive Fibonacci numbers roughly equal the Golden Ratio--especially as the numbers increase in size.
The Golden Ratio also informs the Golden Rectangle, which is considered the most visually satisfying geometric from. The ratio of the length and width of the Golden Rectangle equal the Golden Ratio. The Golden Rectangle is often employed in photography, art, and design (but more on that in a later post).
Outside of the realm of mathematics, the Golden Ratio plays a surprisingly significant role in the natural world. In nature, the Golden Ratio can be found in the arrangement of flower petals in some flowers, seed heads, pinecones, tree branches, shells, spiral galaxies, dolphins, starfish, sand dollars, honey bees, hurricanes, human fingers, and even our DNA molecules.
Moreover, the Golden Ratio, loosely speaking, can be found on the faces of individuals that are generally found most attractive. A geometric “beauty mask” can help predict whether or not the proportions of an individual's face will be deemed attractive by the average person. Of course, we know that beauty comes down to more than a math equation and it's important to promote concepts of beauty that move past traditional definitions--but it's interesting to think about the way this one equation plays such an important but quiet role in our perception of aesthetics.
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Photo: Live Science, Wikimedia Commons