![]() The other methods provide a more efficient way to calculate the accurate value. The more iterations you follow, the closer the approximate value will be to the accurate one. The following table gives the data of calculations for all the assumed values until we get the desired equal terms: Iteration Since both the terms are not equal, we will repeat this process again using the assumed value equal to term 2. ![]() Term 2 = Multiplicative inverse of 1.5 + 1 = 0.6666.Let us start with value 1.5 as our first guess. Since ϕ = 1 + 1/ϕ, it must be greater than 1. For the second iteration, we will use the assumed value equal to the term 2 obtained in step 2, and so on.If not, we will repeat the process till we get an approximately equal value for both terms. Both the terms obtained in the above steps should be equal.Calculate another term by adding 1 to the multiplicative inverse of that value.Calculate the multiplicative inverse of the value you guessed, i.e., 1/value.We will guess an arbitrary value of the constant, then follow these steps to calculate a closer value in each iteration. The value of the golden ratio can be calculated using different methods. Artists like Leonardo Da Vinci, Raphael, Sandro Botticelli, and Georges Seurat used this as an attribute in their artworks. Many architectural wonders like the Great Mosque of Kairouan have been built to reflect the golden ratio in their structure. There are many applications of the golden ratio in the field of architecture. Mentioned below are the golden ratio in architecture and art examples. When a line is divided into two parts, the long part that is divided by the short part is equal to the whole length divided by the long part is defined as the golden ratio. where a and b are the dimensions of two quantities and a is the larger among the two. Thus, the following equation establishes the relationship for the calculation of golden ratio: ϕ = a/b = (a + b)/a = 1.61803398875. It finds application in geometry, art, architecture, and other areas. The approximate value of ϕ is equal to 1.61803398875. ![]() It is denoted using the Greek letter ϕ, pronounced as "phi". Refer to the following diagram for a better understanding of the above concept: The ratio of the length of the longer part, say "a" to the length of the shorter part, say "b" is equal to the ratio of their sum " (a + b)" to the longer length. With reference to this definition, if we divide a line into two parts, the parts will be in the golden ratio if: The golden ratio, which is also referred to as the golden mean, divine proportion, or golden section, exists between two quantities if their ratio is equal to the ratio of their sum to the larger quantity between the two.
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