The contributions of Pingala and Fibonacci are important, but it’s not apparent that anyone even realized its connection to the Golden Ratio until the 1600’s by Johannes Kepler and others. The sequence itself though had been described as early as the 2nd or 3rd century BC in the works of Acharya Pingala, an Indian mathematician who enumerated the possible patterns of Sanskrit poetry that could be formed from syllables of two lengths. Liber Abaci became a pivotal influence in adoption by the Europeans of the Arabic decimal system of counting over Roman numerals. He learned of it though while being educated in North Africa with an Arab master, where he was exposed to the much earlier knowledge of Indian mathematicians. His book Liber Abaci, published in 1202, introduced this sequence to Western European mathematics in the form of a math problem on the breeding of rabbits. What we now as the Fibonacci sequence is named after Leonardo Pisano Bonacci (aka Bigollo) of Pisa, an Italian born in 1175 AD, who later became known as Leonardo Fibonacci. The Fibonacci Sequence was written of in India in about 200-300 BC and brought to the Western world around 1200 AD He also linked this number to the construction of a pentagram. This is analogous to what Euclid later wrote.Įuclid (365 BC – 300 BC), in “Elements,” referred to dividing a line at the 0.6180399… point as “dividing a line in the extreme and mean ratio.” This later gave rise to the use of the term mean in the golden mean. Accordingly it follows, of necessity, that they all turn out to be the same, and since they have all become the same as one another, they will all be one.” Translation © 2021 by David Horan So whenever the middle item of three numbers or volumes or powers is such that the first is to the middle as the middle is to the last, and again, that the last is to the middle as the middle is to the first, then the middle becomes first and last, and the last and first for their part both become middles. The very best bond is that which, as much as possible, makes itself and the conjoined entities, one and it is proportion that by nature best accomplishes this. “Now it is not possible for two things to be combined well on their own without a third, for some bond is required between the two to draw them together. It was not known as the golden ratio in his time, but he describes it with his first reference to proportion: Plato (circa 428 BC – 347 BC), in his views on natural science and cosmology presented in his “Timaeus,” considered the golden ratio to be the most binding of all mathematical relationships and the key to the physics of the cosmos. Phidias (500 BC – 432 BC), a Greek sculptor and mathematician, studied phi and applied it to the design of sculptures for the Parthenon. The Greeks are thought by some to have based the design of the Parthenon on this proportion, but this is subject to some conjecture. It appears that the Egyptians may have used both pi and phi in the design of the Great Pyramids. Uses in architecture potentially date to the ancient Egyptians and Greeks It is reasonable to assume that it has perhaps been discovered and rediscovered throughout history, which explains why it goes under several names. While the proportion known as the Golden Mean has always existed in mathematics and in the physical universe, it is unknown exactly when it was first discovered and applied by mankind.
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