math final final - 2 The Golden Ratio The Golden Ratio Katrina Gossage Southern New Hampshire University 2 The Golden Ratio This paper will be

# math final final - 2 The Golden Ratio The Golden Ratio...

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2The Golden RatioThe Golden RatioKatrina GossageSouthern New Hampshire University
2The Golden RatioThis paper will be discussing the golden ratio, and will be discussing multiple terms related to it. The first to define the golden ratio was Euclid, in his book of Elements. However, it is believed the golden ratio can be seen well beforethis, such as with the Parthenon statues, created by Phidias. The golden ratio can be seen in many things, from shells to the milky way in the galaxy. One person who made history with the use of the golden ratio was Fibonacci, in which the numbers of the golden ratio where named after. The golden ratio has been used threw out history, which has led to many different discoveries, and now today, whether or not we are aware of it, we can see the golden ratio all around us as a part of many different things.The first definition of the golden ratio came from Euclid. Euclid is known as the father of geometry and also wrote the book Elements (Greek: Στοιχεα), around 300 BC. In this book he defined the golden ratio as “extreme and mean ratio” (Livio, 2003). According to Euclid, as indicated in the book Elements, by Euclid & Heath (1956):"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." In Elements Euclid offers many hypothesis and how these hypotheses demonstrate the golden ratio. Upon examination of these hypothesizes it can be seen that some present the golden ratio as an irrational number (Stakhov & Olsen,2009).
2The Golden RatioIn the book Elements Euclid says, “the line AB is divided in extreme and mean ratio by C if AB:AC = AC:CB”(Euclid &Heath, 1956). Although Euclid didnot indicate this to be the golden ratio we will call this the Golden ratio. It is believed the golden ratio is not the original work of Euclid, that it was studied before, but the question still remains as to who. Related to the golden ratio, Euclidalso indicates, in Elements, how Plato’s platonic solids are related to the golden ratio (Livio, 2003).Plato’s interest was explaining how the universe worked and how it came to be. Plato hypothesized that matter was organized into five regular solids. These solids are the cube, tetrahedron, icosahedron, octahedron, and the dodecahedron. Plato and his students thought water, earth, air, and fire where the four basic elements of matter. The argument for this is that each element corresponded with one of the solids, with each of these solids having dimensions that are related to the golden ratio (Livio, 2003).The interest that grew from Plato, about the golden ratio, is what lead to itsdefinition, in the book of Elements written by Euclid. Plato was a Greek philosopher, Socrates student, mathematician, philosophical writer, and most importantly created the first higher learning institute in the western world.It can be seen that the golden ratio was discussed, but not yet defined by Plato (Livio, 2003). For example, in a dialog Plato wrote, called Timaeus (Greek: Τίμαιος,

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• Spring '16
• Tamara Eyster
• Math, Golden ratio, Livio