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),

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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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