The Importance Of 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.

By this time, numbers and geometry had acquired a metaphysical significance and were believed to have occult symbolism and power. The introduction of sacred geometry into all aspects of the design of places of worship was therefore inevitable and from that time key design features such as the numbers of pillars in the choir, the layout of the floor plan and

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

For this reason, the Greeks quickly realized that a solution to irrational numbers was imperative. Fortunately, Eudoxus was able to present a new theory of proportions which did not involve numbers. “Instead, he studied geometrical objects such as line segments, angles, etc., whiling avoiding giving numerical values to lengths of line segments, sizes of angles, and other magnitudes.” (Lecture 8. Eudoxus, Avoided a Fundamental Conflict)

It was the widespread math system in the ancient time, and it was utilized to distinguish things that had a great sense of similarity. The methodology was dependent on the capabilities of an individual to recognize the shapes and sizes of the things that are in question. Moreover, the ancient persons also evaluated the design and the material composition of their belongings to know their numbers. As a matter of fact, individualization was an imperative math system that was largely accommodated in the ancient society. The style was dependent on the degree of the experience a person had with his or her commodities or domestic possession. For example, the hunter was familiar with diverse rivers in his neighborhood; hence, it was not worth for him to identify their

This article describes the aesthetically pleasing number, phi. The number phi can be known as (1+√5)/2 or 1.6180….. Why is phi pleasing? For example, if you have a rectangle with the ratio of the sides, the closer the ratio is to phi, the more pleasing it will be. Phi occurs everywhere; a seashell’s spirals, the arrangement of leaves on a plant stem, and even in black holes. This article has many examples on how to see phi in real life or just to learn how to use phi.

Fibonacci sequence can have a connection with piano scales. Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89………… The C scale has 13 keys. The ratio is close to 0.618, this is known as the golden rule.

The golden ratio can be applied in many different areas of our world from space to the shells of snails. It can be found in the architecture of the Greek and Roman structures and monuments and also in the modern buildings and structures around the world. Ancient Egyptians and Greeks used the golden ratio for art, architecture and sculptures. The ancient Egyptians viewed this number as a divine number and incorporated it

My example of irrational numbers is the Golden ratio from the Fibonacci sequence. The Fibonacci sequence starts as 0, 1, 1, 2, 3, 5,... The numbers are added together to get the next sequence number. was made famous during the 13th century by Leonardo Pisano. The Golden ratio is when you take the sequence numbers and divide each by the previous number. The Golden ratio is the final set of numbers in, "the following set of numbers: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666..., 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.61538..." (Knott, 2013). The Greek letter Phi is the represented symbol for the Golden ratio (1.61538...) This number is the reason for, " the spirals in the seedheads and the arrangements of leaves in many plants."(Knott, 2013). The

Why, how, and what are what is referred as the Golden Circle. According to Simon Sinek (2009), the Golden Circle is what finds order and predictability in our behavior. It allows us to understand why we do what we do. The most important part of the Golden Circle is: Why. Everyone knows what he or she does and most people

The Protogeometric and Geometric periods are good examples of such advanced thinking. The beginnings of the Protogeometric period display a distinct interest in mathematical order. During this period, artists decorated vases with circles and symmetrical patterns. As the dominant style changed from Protogeometric to Geometric, this order and precision was amplified. The popular ?circle and semicircle patterns were replaced by linear designs, zigzags, triangles, diamonds, and meanders? (Cunningham, 40). The increased interest in order seems to have been a reflection of the Greek fascination with nature, and man?s relationship to nature.

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

The Egyptians used sums of unit fractions (a), supplemented by the fraction B, to express all other fractions. For example, the fraction E was the sum of the fractions 3 and *. Using this system, the Egyptians were able to solve all problems of arithmetic that involved fractions, as well as some elementary problems in algebra. In geometry, the Egyptians calculated the correct areas of triangles, rectangles, and trapezoids and the volumes of figures such as bricks, cylinders, and pyramids. To find the area of a circle, the Egyptians used the square on U of the diameter of the circle, a value of about 3.16-close to the value of the ratio known as pi, which is about 3.14. The Babylonian system of numeration was quite different from the Egyptian system. In the Babylonian system-which, when using clay tablets, consisted of various wedge-shaped marks-a single wedge indicated 1 and an arrowlike wedge stood for 10 (see table). Numbers up through 59 were formed from these symbols through an additive process, as in Egyptian mathematics. The number 60, however, was represented by the same symbol as 1, and from this point on a positional symbol was used. That is, the value of one of the first 59 numerals depended henceforth on its position in the total numeral. For example, a numeral consisting of a symbol for 2 followed by one for 27 and ending in one for 10 stood for 2 × 602 + 27 × 60 + 10.

In the ancient times, the Golden Ratio was the most used mathematical tool. The Golden Ratio is a term used to describe aesthetically pleasing proportioning within a piece. It is an actual ratio 1: PHI. The Golden Ratio was a tool used for composition, not rule. It was often used by Leonardo Da Vinci in several of his paintings. All key dimensions of the room and table in Da Vinci’s “The Last Supper” were based on the Golden Ratio, known as the Divine Proportion in the Renaissance. In Michaelangelo’s painting of “The Creation of Adam” the finger of God touches the finger of Adam precisely on the golden ratio point of the width and height on the area that contains them both. Botticelli compared “The Birth of Venus” with several different golden ratio points, all coming to the woman’s naval and bottom tip of her right elbow. The well known French painter, Georges Pierre Seurat, was notorious for “attacking every canvas by the golden section.” In one of his paintings, the horizon falls exactly on

The first man to really make an impact in the calculation of pi was the Greek, Archimedes of Syracuse. Where two people by then name of Antiphon and Bryson left off with their inscribed and circumscribed polygons, Archimedes took up the challenge. However, he used a slightly different method than they used. Archimedes focused on the polygons' perimeters as opposed to their areas, so that he approximated the circle's circumference instead of the area. He started with an inscribed and a circumscribed hexagon then doubled the sides four times to finish with two 96-sided polygons. Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed. Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower