Taking a Look at the Golden Ratio

Sinek (2011) writes, “The Golden Circle was inspired by the golden ratio- a simple mathematical relationship that has fascinated mathematicians, biologists, architects, artists, musicians and naturalist since the beginning of history” (Sinek, 2011, p. 37). The Golden Circle, as shown in figure 1, is comprised of three circles: The outermost ring is the “What,” this is what the company does to fulfill their core belief. The next ring is the “How,” this is how the business achieve their core belief. Finally, the innermost ring is the “Why,” this is the core belief of the business. It is why the business exists. Sinek uses the Golden Circle to illustrate how many companies begin with what they do, instead of why they do it.

The golden ratio or the divine proportion is connected to Phi. Phi’s number rounded to the thousandths place is 1.168. Phi is from the Greek alphabet. “To take an example: you might not suspect, unless you had some acquaintance with the golden rectangle, that lopping off a square from it leaves a residue which is another golden rectangle, and that this process can be repeated indefinitely

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

What is a ratio?  What are the different ways of expressing the relationship of two amounts?  What information does a ratio provide?

Rand likely named The Golden One after Gaea because, like the earth goddess, she would come to be the mother of all that is new. The society Prometheus intends to create cannot flourish without new generations, and she is the only one who can make that happen.

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

“Pi is the ratio of the circumference of

Gold was discovered in 1847 by General John A. Sutter. Gold was found in a saw mill. They noticed something shiny at the bottom of a ditch. Once they discovered it was gold they dug more and found a lot of it. Gold’s symbol is Au, the Atomic number is 79, the average atomic mass is 196.967, gold-179. 36 is the only naturally occurring isotope of gold, its state of matter is solid, and it is not synthetic.

Archimedes produced formulas to find the area of regular shapes by using the shapes he already knew how to calculate (The History of Archimedes). An example of this would be the circle. Archimedes would draw a polygon on the outside of the circle and then a smaller one on the inside and he would solve the area of the polygons. Although he knew this only would only get him a range and that the actual calculation might never be found (The History of Archimedes). He similarly was able to find the calculation of the volume of a sphere. He did this by cutting the sphere into a series of cylinders, (The History of Archimedes) and then adding the volumes of the cylinders. Archimedes noticed that the smaller he cut the cylinders the more accurate. His approximation eventually became an exact calculation. Despite all of Archimedes’ contributions to mathematics, the story he is probably the most well-known for would be his discovery of a method for finding the volume of an object with an irregular shape (The History of Archimedes). Hiero had asked the royal goldsmith to fashion a new royal crown for him. Hiero provided a thing of gold to make it, but once Hiero was given his newly made crown he began to believe that the goldsmith cheated him out of some of his gold a replaced it with silver. He asked Archimedes if he could determine this. So while bathing Archimedes noticed

Mathematical concepts that we know and use nowadays are thanks to contributions made from different mathematicians throughout time. The Medieval Times are no exception since great men living in this era contributed to the beautiful subject of mathematics. Some of the many intelligent minds from this era

To the Egyptians, gold represented perfection, so they gave it the symbol of a circle. Since Silver was the closest to gold in perfection, it was given the symbol of a semi-circle. Later this semi-circle led to a growing moon symbol.

The ratio between two Fibonacci numbers is very close to the golden ratio, which is 1+521.61803399. The table and graph below demonstrate this. In the table, I found the ratios by dividing a Fibonacci term by the one before it and then subtracted that from the golden ratio to find the deviation. For example, consider the third Fibonacci term, 2, and the second term, 1. The ratio between the two is 21=2. The deviation from the golden ratio is 2-1.61803399=0.38196601.

The Pythagoreans were a group of people who followed Pythagoras in 530 B.C. They are well known for their work in mathematics and for numerology, they tried to prove that everything is made up of numbers. The Pythagoreans tried to solve the problem of Anaximander by the theory of the Limit which was the flaw in Anaximander’s theory.

Balance can be found in many artworks and architecture as artists and designers applied Phi in their works. Phi, (1.618 in Mathematics and science) is the 21st letter of the Greek alphabet and may also be known as the golden ratio, divine proportion or golden proportion. According to Gary Meisner, “Many artists and architects have proportioned their works

From it being shown at Temple Delphi, the Golden Mean has been adopted into various Greek Myths and teachings. One of the most known myths that exhibits characteristics of the Mean is Icarus’s Fall. (Icarus’ Fall: “The Myth, Symbol, and Interpretation”) In that myth, Icarus and his father Daedalus are incarcerated on the island of Crete after building a Labyrinth that houses