Golden Ratio
The Golden Ratio Body, art, music, architecture, nature – all connected by a simple irrational number – the Golden Ratio. According to Posamentier & Lehmann in their work The
(Fabulous) Fibonacci Numbers, there is reason to believe that the letter φ (phi) was used because it is the first letter of the name of the celebrated Greek sculptor Phidias (490-430 BCE). He produced the famous statue of Zeus in the Temple of Olympia and supervised the construction of the Parthenon in Athens Greece (Posamentier & Lehmann, 2007). In constructing this masterpiece building, Phidias used the Golden Ratio to create a masterpiece of work.
Figure 1: This is a model of Zeus in the Temple of Olympia. The red lines show the use of the Golden Ratio. (www.scarletcanvas.com/)
Phidias brought about the beginning of the one of the most universally recognized form of proportion and style used throughout history (Posamentier & Lehmann, 2007). The irrational number Phi, also known as the Golden Ratio, has had tremendous importance. To properly understand this mathematical concept, it is important to explore the definition, history, and the relations to architecture, art, music and the Fibonacci sequence.
Figure 2: This model shows the line segments in the Golden Ratio. (Wikipedia.org)
As is with any new topic, it is essential to have a foundational understanding. According to Wikipedia, the definition of the Golden Ratio: In mathematics and the arts, two quantities are in the Golden Ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure on the left illustrates the geometric relationship (Wikipedia.org). In a documentary from the Discovery Channel titled, “Assignment Discovery: The Golden Ratio”, the narrator explains the Golden Ratio as; “the ratio of the whole segment to the larger piece is equal to the ratio of the larger piece to the smaller piece (see figure
(Fabulous) Fibonacci Numbers, there is reason to believe that the letter φ (phi) was used because it is the first letter of the name of the celebrated Greek sculptor Phidias (490-430 BCE). He produced the famous statue of Zeus in the Temple of Olympia and supervised the construction of the Parthenon in Athens Greece (Posamentier & Lehmann, 2007). In constructing this masterpiece building, Phidias used the Golden Ratio to create a masterpiece of work.
Figure 1: This is a model of Zeus in the Temple of Olympia. The red lines show the use of the Golden Ratio. (www.scarletcanvas.com/)
Phidias brought about the beginning of the one of the most universally recognized form of proportion and style used throughout history (Posamentier & Lehmann, 2007). The irrational number Phi, also known as the Golden Ratio, has had tremendous importance. To properly understand this mathematical concept, it is important to explore the definition, history, and the relations to architecture, art, music and the Fibonacci sequence.
Figure 2: This model shows the line segments in the Golden Ratio. (Wikipedia.org)
As is with any new topic, it is essential to have a foundational understanding. According to Wikipedia, the definition of the Golden Ratio: In mathematics and the arts, two quantities are in the Golden Ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure on the left illustrates the geometric relationship (Wikipedia.org). In a documentary from the Discovery Channel titled, “Assignment Discovery: The Golden Ratio”, the narrator explains the Golden Ratio as; “the ratio of the whole segment to the larger piece is equal to the ratio of the larger piece to the smaller piece (see figure
Bibliography: Adam, J. (2003). Mathematics in nature: Modeling patterns in the natural world. Princeton, NJ: Princeton University Press. Assignment discover: The golden ratio (2011) Byron, D. (1996, Februray 15). Golden ratio and golden rectangle. Retrieved from Math Forum: http://mathforum.org/library/drmath/view/59031.html Dunlap, R Golden ratio. (2012). Retrieved from http://en.wikipedia.org/wiki/ Golden_ratio Harris, W Jovanovic, R. (2003). Golden section. Retrieved from Milan Milanovic http://milan.milanovic .org/math/english/golden/golden1.html. Kalajdzievski, S. (2008). Math and art an introduction to visual mathematics. Boca Raton, FL: Taylor & Francis group. Pickover, C. (2012). The math book. New York: Sterling Publishing Co., Inc. Posamentier, A. S., & Lehmann, I. (2007). The fabulous fibonacci numbers. Amherst, NY: Prometheus Books. Wolfram Alpha LLC Yurick, S. (2011). Music and the fibonacci series. PhiPoint Solutions, LLC.