# Understanding the Fibonacci Number Sequence

Co-author Terry Hurley

The discovery of the Fibonacci number system began with a simple mathematical question: If you start with only one pair of rabbits, how many pairs of rabbits will you have at the end of one year? No one knew at the time that the answer to this problem would become referred to as nature's numbering system, the Fibonacci sequence.

## Fibonacci Number Sequence

The now famous recreational mathematical problem about the rabbits first appeared in the book, Liber Abaci or Book of Calculation, written in 1202 by Leonardo da Pisa, also known as Fibonacci. The problem solution, the Fibonacci number series is a sequence of numbers where the sum of any two consecutive numbers is equal to the number that follows it. Beginning with the number 1, the Fibonacci sequence numbers are: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and continues on in this way infinitely.

### Relationship to Phi

Another interesting aspect of the Fibonacci sequence of numbers is its unique relationship to phi. Although phi is an infinite number, for many purposes it is commonly carried out to the third decimal place. The ratio of any two consecutive numbers in the Fibonacci sequence equals almost exactly phi, or 1.618. For example:

• 21 divided by 13 equals 1.615
• 233 divided by 144 equals 1.618
• 610 divided by 377 equals 1.618

After the fortieth number in the Fibonacci sequence, the number for the ratio of phi is accurate to the fifteenth decimal place.

## Phi and the Golden Ratio

Known as nature's perfect number, 1.618 or phi, is the number of the Golden Ratio, which is the ratio that exists between two quantities and their relationship to one another. No one knows for certain when the actual mathematical discovery of phi took place. It is known that it was used by the ancient people such as the Egyptians in the building of the pyramids and the Greeks in the building of the Parthenon.

### Fibonacci Sequence in Everyday Life

The Golden Ratio plays an integral part in all aspects nature and life. It is found in almost everything that exists in the universe, and the universe itself. It is found in:

• All forms of life
• Architecture
• Music
• Nature
• Science
• The arts

## The Fibonacci Number Sequence and Feng Shui

As shown in the ancient Chinese text the Zhouyi, the early Chinese people recognized nature's patterns and wrote down their findings. Zhouyi is the name for the Yijing, also called the Book of Change or I Ching, before the Han Dynasty. In the famous oracle, people recorded the conditions of the universe and the conditions that they experienced.

Attributing their knowledge to their gods, these ancient people understood that the universal energy of qi (chi) was associated with numbers. These ancient people developed the system of feng shui based on the mathematical patterns they saw and experienced in nature. Several of the core principles of feng shui also correspond to the numbers of the Fibonacci sequence:

• Number 1: Taiji which means center
• Number 2: Yin and Yang
• Number 3: Loushu Magic Square, also known as the Magic Square of Three or bagua, and the cosmic trinity of heaven, earth and human qi
• Number 5: Five elements or five phases which are earth, fire, water, wood and metal
• Number 8: Eight trigrams or directions

## Achieving Balance and Harmony

The Golden Ratio and the Fibonacci number sequence are important concepts to the practice of feng shui since it relates to the delicate balance of the elements and the harmony that must exist between human life and the environment. They also bring to light the importance of focusing on the perception of perfection in the shape of objects used in living spaces and how these must also provide a natural balance of the universal energy of life.