Hi. This page will be about the golden ratio based on the Fibonacci sequence.

Recall that the Fibonacci sequence of numbers is an infinite (never-ending) sequence of numbers. Here are some of the starting terms of the Fibonacci sequence (beginning with 1 and 1).

**The Road To The Golden Ratio**

The golden ratio can be achieved from the Fibonacci sequence of numbers by obtaining ratios of two successive numbers.

The ratio of the first two terms is . The ratio of the second number and the third number with the more recent number as the numerator is . The ratio of the fourth number over the third number is . We continue the pattern and notice that we eventually reach a number. Refer to the chart below.

We could continue the chart but since the Fibonacci sequence of numbers is never-ending (infinite) our chart would be never ending as well. We notice that the ratio reaches the number of 1.618 (to 3 decimal places). This number is referred to as the golden ratio.

The golden ratio is an irrational number as it is not a whole number and it has a never ending amount of decimal places. The irrational number Pi also has a never ending amount of decimals places with .

From the golden ratio, we can achieve the golden mean which is the reciprocal of the golden ratio. The reciprocal of 1.618 is