One of the most remarkable discoveries in mathematics is known as the Golden Ratio. Since its finding, it has been seen a number of times in mathematics, nature, art, and architecture. The Golden Ratio is, as its name implies, a ratio. That is, it demonstrates the relationship between two quantities of the same kind. When finding the Golden Ratio, two ratios are compared. More specifically, if the ratio of the sum of two amounts compared to the larger amount is equal to the ratio of the larger amount to the smaller one, the value is considered part of the Golden Ratio. So, if you have a line that is divided into two parts, the Golden Ratio can be seen if the entire length of the line divided by the longer part of the line is equal to the longer part of the line divided by the smaller part (Markowsky 2). If we let a equal the larger part and b equal the smaller part, we can represent the Golden Ratio in a formula as =. The value of the Golden Ratio is usually approximated at 1.618 therefore the Golden Ratio is 1:1.618. Just like pi, its value is rounded off because it is a irrational number since its digits continue infinitely with no repeating pattern. It is symbolized by the Greek letter phi, φ (Markowsky 3).
As stated before, the Golden Ratio can be witnessed in many different instances. In mathematics, it is connected to the Fibonacci Sequence. The Fibonacci Sequence, as we learned in class, begins with 1 as the first two numbers of the sequence. We can find the third number of the sequence by adding the two previous numbers, 1+1=2. The following numbers of the sequence can be found by continuing this pattern of adding the two previous numbers. Therefore, the Fibonacci Sequence looks like this 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. If you divide each number by the one right before it, like 1/1, 2/1, 3/2 and so on, we get a new sequence of 1, 2, 1.5, 1.667, 1.6, 1.625, 1.615, 1.619, 1.6176, 1.6181, 1.6179, etc (Carlson). Eventually, the Golden Ratio can be observed in this sequence by dividing the 39th number by the 38th number in the sequence, 63,245,986/39,088,169. This connection, however was not intentional when Fibonacci invented his sequence and, in fact, was unknown to him, but is now a very fascinating find.
In architecture, the Golden Ratio was used by Greek sculptor Phidias in the design of the Parthenon, who supervised its building. In art and architecture, the Golden Ratio is said to be most pleasing to the eye. For that reason, it was used in many aspects in the construction of the building. The Golden Ratio is used to form the golden rectangle, with the height being 1 and the width being 1.618. A golden rectangle can be produced around the Parthenon, with its triangular