Derive the golden section from the following relationship of ratios: a+b/a = a/b. For these ratios, imagine that you have a line that is 100 inches long. This value is a+b. Now, divide the line into two parts so that the ratio of the total length to the long portion (a) is the same as the ratio of the long portion to the short portion (b). For both ratios to be equal, the long portion must be approximately 61.77 inches and the short portion must be approximately 38.22. 100 (a+b) divided by 61.77 (a) is equal to 61.77 (a) divided by 38.22 (b). Both values are approximately 1.618. In order to get closer to the golden section, you must use much larger values.
Calculate the golden section from the Fibonacci series. The Fibonacci series begins with 0 and 1. These two numbers are added together to get the third number, 1. After this, add the last two numbers in the series to get the next number. Following this principle, you generate the numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, etc. To get the golden section from these numbers, divide two adjacent numbers. The larger the numbers, the closer you will get to the golden section. For example, 3 divided by 2 is 1.5. Using much larger numbers in the series, 377 and 233, you get 1.618.
Use the traditional formula. Add 1 to the square root of 5 and divide the sum by 2. This formula gives the most precise calculation.