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Educational => Mathematics => History of Mathematics => Topic started by: Masuma Parvin on January 13, 2015, 04:49:03 PM

Title: The History of Phi & The Golden Ratio
Post by: Masuma Parvin on January 13, 2015, 04:49:03 PM
The Golden Ratio – Phi - is known by many other names such as; The Golden Section, Golden Number, Golden Mean, Golden Proportion, Golden Rectangle, Golden Triangle, Golden Spiral, Golden Cut, The Divine Proportion, Fibonacci Sequence, and Tau (τ).
Who first discovered The Golden Ratio?
No one really knows for sure as to who originally discovered the The Golden Ratio – 1.618 - (a.k.a. the Phi ratio) in Human history, but some suggestions point to the ancient Egyptians and even as far back as the ancient Sumerian civilization. However, the ratio was also used by many artists, mathematicians, scientists and philosophers throughout history. The most renowned include the Greeks, such as:

Pythagoras (570–495 BC) was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He is best known for the Pythagorean theorem which bears his name to this day. Although, because legend and obfuscation cloud his work even more than with the other pre-Socratic philosophers, one can say little with confidence about his teachings, and some have questioned whether he contributed much to mathematics and natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.
Pythagoras thought that absolute happiness lay in the contemplation of the harmony of the rhythms of the Universe, (“tes teleiotetos arithmon”- the perfection of numbers, the number being both rhythm and proportion). In other words, Pythagoras was looking for a numerical pattern that would explain it all. A goal of Pythagoras’ disciples was to develop a ratio theory. The ratio, a comparison between two sizes represented in mathematics a basic operation of judgment: the perception of the relation between ideas.
Title: Re: The History of Phi & The Golden Ratio
Post by: Masuma Parvin on January 13, 2015, 04:49:42 PM
Hippocrates of Chios (470–410 BC) was an ancient Greek mathematician, (geometer), and astronomer. He is reported to have been kicked out of a secretive group for having divulged the construction of the pentagram. The pentagram and pentagon are constructed using Phi ratios (as well as deriving Phi from these geometric shapes; as I also discovered for myself back in 2004 and is mentioned under the article “What Followed After My Discovery of OneEye“). Supposedly, the construction of the pentagram or pentagon was one of the secrets of the Medieval Mason’s guilds. The Pentagram was used as a sign of salutation by the Pythagoreans, its construction supposed to have been a jealously guarded secret.
Phidias (490–430 BC) was a Greek sculptor, painter and architect, who lived in the 5th century BC and is said to exhibit Phi ratios in his body of artistic works without a mention of using mathematics. He made the Parthenon statues that seem to embody the Golden Ratio.
Title: Re: The History of Phi & The Golden Ratio
Post by: Masuma Parvin on January 13, 2015, 04:51:41 PM
Plato (428–347 BC) was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world.
He wrote a dialogue named Timaeus (Greek: Τίμαιος, Timaios) one of Plato’s dialogues, mostly in the form of a long monologue given by the title character, written circa 360 BC. The work puts forward speculation on the nature of the physical world and human beings. [source]
“For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean—then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one”; thereby he implies the aesthetically perfect proportion known as Golden ratio or Golden mean. (31c – 32a).” [source]

Euclid (323–283 BC) is often referred to as the “father of geometry”, where he wrote the collection of 13 books named “The Elements” and was written in Greek around 300 BC. In “The Elements”, he gave the first recorded definition of the golden ratio, which he called, as translated into English, “extreme and mean ratio”.
Many historians do not believe that Euclid’s Elements represents his original work so there is the question of who studied the golden ratio before Euclid. Proclus, a Greek mathematician who lived several centuries after Euclid, wrote in his commentary of the Elements:
“Euclid, who put together the Elements, collecting many of Eudoxus’ theorems, perfecting many of Theaetetus’, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors”