Running head: FIBONACCI AND THE GOLDEN RATIO Kayla Adams Fibonacci and the Golden Ratio Southern New Hampshire University
1 FIBONACCI AND THE GOLDEN RATIO Introduction Leonardo of Pisa is a 13 th Century Italian mathematician better known by Fibonacci. He was arguably the most talented mathematician of his time. Little is known of his childhood, however his largely influential book, Liber Abaci , was widely adopted through Europe and changed the mathematics system. Fibonacci is best known for his introduction of a particular number series, known as the Fibonacci Sequence. Fibonacci discovered a sequence of numbers that closely relates to the Golden Ratio, which is one of the most outstanding discoveries in mathematics. The Fibonacci Sequence, along with the Golden Ratio, unveils itself in art, nature, and architecture. Part 1 Euclid of Alexandria Who is Euclid of Alexandria? A controversial topic to some. Was he a historical mathematician who wrote the Elements? Or was Euclid the leader of a team of mathematicians working along him in Alexandria? Lastly, was Euclid in fact not a person? But, a group of mathematicians whom worked under the name Euclid, a historical character derived from Euclid of Megara, a philosopher who lived one hundred years prior (O’Connor & Robertson, 1999). All controversy aside, Euclid is noted to be the author of the mathematical and geometric treatise known as Elements. The Elements is a thirteen volume series consisting of “definitions, postulates, common notions, propositions and lemmata (i.e. theorems and constructions),
2 FIBONACCI AND THE GOLDEN RATIO corollaries and mathematical proofs of the propositions” that has been used as an educational foundation in mathematics for the past two thousand years (bookofproofs, 2014). In one of the volumes, Euclid was the first to write the definition of what is now called the Golden Ratio. Euclid explains that line AB is divided in “extreme and mean ratio” by finding the golden section (Knott, 2016). Euclid defined it as, “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 lesser” (Livio, 2002). Therefore, if you take a line segment and divide it into two smaller segments, the larger segment divided by the smaller segment is equal to the full line segment divided by the smaller segment (O’Conner & Robertson, 2001). The Golden Ratio is now represented as the Greek letter “Phi”, which represents the approximate number 1.618. The Golden Ratio is known to be aesthetically pleasing, found in both notorious historical art pieces and architecture, as well as in nature (Burger & Starbird, 2013, p. 59). Although it is uncertain exactly who Euclid was, it is without a doubt The Elements is the most influential compilation of mathematics studied by many future mathematicians.
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