The Fibonacci Series, Phi, Shapes, and Numbers: Sacred Geometry in Nature and Culture

For eons, human beings have felt that certain numbers, ratios, and shapes have sacred significance. For instance, the number ‘7’ has had great significance in various aspects of many cultures, geometric shapes have been associated with numbers, and the Fibonacci series and Golden Ratio are still instrumental in everything from Art to Music.

Sacred Meanings in Geometric Numbers and Shapes

Symbolic and sacred meanings are also ascribed to certain geometric
numbers, shapes, and geometric ratios or proportions. Through the ages, especially in the ancient world, some numbers had symbolic meaning attached, aside from their ordinary use for counting or calculating. In geometry, figures such as triangles, squares, polygons, hexagons, and so forth are all related to numbers. Triangles, for example, relate to three angles, squares to four, and so on.
As an example of attaching sacred meanings to geometric numbers, the number ‘seven’ occurs consistently in diverse cultures around the world. And more, the religious and mythologies of the world are filled with sevens. Consider some of these:

Pyramids of Giza: Image by Darren Krape

• The shape of the pyramids of Egypt produces the number seven by combining the three-sided triangle and four-sided square.
• In music, the seven musical notes in a scale repeat at the octave.
• There are seven terraces of purgatory in the Roman Catholic beliefs.
• The Christian Church recognizes the seven virtues and seven deadly sins.
• There were seven steps taken by Buddha at his birth.
• There are seven heavens and seven earths in Islamic tradition.
• There are seven worlds in the Hindu universe.
• The seven-branched Jewish menorah is the oldest symbol in Judaism.

The ancient Greek philosopher Pythagoras believed that integers represented fundamental meanings. He regarded seven as the “vehicle” of life. To him, the number seven signified the union of spirit and matter – the union of three (the triple nature of the spirit) combined with the four elements of matter (earth, air, fire, and water).
Seven was also associated with growth, whereby a phenomenon tends to be completed in seven stages, such as the “seven stages of man” expressed by Shakespeare in  As You Like It, or the biblical Creation by God in seven days. According to some beliefs, the human body needs seven energy vortices known as chakras to be open for spiritual growth; that is, one has to move focus from the three lower (physical) chakras to the four higher (spiritual) centers.

The Fibonacci Sequence is present in the nautilus shell. Image by jitze

How then is the Fibonacci sequence related to Sacred Geometry? The Fibonacci sequence is a series of numbers in which each number is the sum of the previous two. It starts with 0 and 1,which equals 1. Then 1 plus 2 equals 3, 2 plus 3 equals 5, and so on. Why are these numbers significant? Simply, they are nature’s numbering system and they give rise to the mystical Phi, what is referred to as the “golden section” or “golden ratio.” It should be noted that the ratio of successive pairs from the Fibonacci series tends toward Phi or 1.618 and out of this ratio comes the golden rectangle and the spiral shape, which is the most widespread shape in the universe.
The Fibonacci numbers are represented practically everywhere. In the petals on a flower, or the arrangement of leaves along a stem, you will find this sequence of numbers. The petals on most flowers display one of the Fibonacci numbers. The numbers also appear in certain parts of sea shell formations. Parts of the human body also reveal these ratios, including the five fingers, and a thumb on each hand. Fibonacci also can be seen in a piano that produces harmony through a beautiful music. A piano has one keyboard with five black keys (sharps and flats) arranged in groups of two and three, and eight white keys (whole tones) for the 13 chromatic musical octaves.
The Phi or 1.618 was described in the past as a divine number because it signifies beauty and harmony. Egyptian architects made use of Phi relationships in the construction of temples and the Great Pyramid, and so did the Greeks in their Parthenon in Athens, and the Europeans, for their Gothic cathedrals.

The Sacred Geometry

Simply described, the Sacred Geometry arises out of the set of numbers from the Fibonacci series or the “golden ratio.”  Through the years since ancient times, it has been significantly used in the planning and construction of religious structures (churches, temples, mosques, tabernacles, altars and monuments), as well as sacred spaces (like holy wells and sacred groves), and the creation of religious art.
Consciously or not, humans seem to be genetically programmed to respond to these sacred numbers, ratios, and shapes. Thanks to Italian mathematician Leonardo Fibonacci for introducing his famous Fibonacci sequence, its associated mystical ratio, the Phi, and paving the way for the shapes that greatly defined the world’s magnificent structures and amazing wonders.

The Fibonacci Sequence appears in both art and nature. Image by labcstm

Fibonacci numbers, ratios and shapes have been used to explain creation, growth and harmony – from a number of petals on a flower and grandiose architecture, to a spiraling galaxy. And to music lovers, it’s one beautiful harmony of musical scale that pleases the ear and ultimately the spirit.  A sacred geometry!

Sources:

Bradley, P.  Great Mysteries. New Holland (2010).

Calter, P. Polygons, Tilings, & Sacred Geometry. Dartmouth. Accessed September 22, 2011.

Sacred Geometry. Spiraloflight. Accessed  September 22, 2011.