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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 has been 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). 

The Seven Chakras

The number 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 Chakras from bottom to top: 
Root, Sacral, Solar Plexus, 
Heart, Throat,
Crown.


The Fibonacci Sequence (The Pi and the Phi)

In geometry, the symbol Φ or φ (phi) represents the Golden Ratio, also known as the golden mean or divine proportion. This number is approximately equal to 1.61803398875. It appears frequently in geometry, art, architecture, and nature, often in relation to aesthetically pleasing proportions.

Aryabhata, in the 5th century CE (refers to "Common Era", the same years as AD does, but in a more secular way), calculated Pi to four decimal places (3.1416), while Brahmagupta introduced the symbol for zero and developed formulas to approximate Pi. With these contributions, Indian mathematicians were able to utilize Pi in a wide array of fields, including astronomy, geometry, and trigonometry.

Pi (π) and Phi (Φ), also known as the Golden Ratio, are two fundamental mathematical constants. Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159. The Golden Ratio, approximately 1.618, is found by dividing a line into two segments such that the ratio of the whole line to the longer segment is equal to the ratio of the longer segment to the shorter segment.


Fibonacci Blocks

The Sacred Geometry

How then is the Fibonacci sequence related to Sacred Geometry? The Fibonacci sequence, discovered by Fibonacci, 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, 3 plus 5 equals 8, and so on. Why are these numbers significant? Simply, they are nature’s numbering system and they give rise to the mystical Phi, 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, we 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 can also 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.

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.

 



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. To music lovers, it’s one beautiful harmony of musical scale that pleases the ear and ultimately the spirit.  
 


 
Resources:

Bradley, P.  Great Mysteries. New Holland (2010).
Corbalan, Fernando. The Golden Ratio. RBA Coleccionables, S.A. (2012)
Devlin, Keith. The Man of Numbers. Bloomsbury (2011)
Livio, Mario. The Golden Ratio. Broadway Books (2002)
Sacred Geometry. Wikipedia. Accessed  September 23, 2011.
"The Parthenon and Phi". The Golden Ratio. By Gary Meisner. Accessed September 23, 2014 
"Phi: The Golden Ratio". What is the Golden Ratio. Live Science. 
 
 
(c) September 23, 2012. Tel Asiado. Inspired Pen Web. All rights reserved.  

David Buick

Science / Inventor Datebook: September 17

American Motor Inventor

David Dunbar Buick (September 17, 1854 – March 5, 1929) was an American inventor born in Scotland. He is best known for founding the Buick Motor Company.

He was born in Arbroath, Angus, Scotland. The family moved to Detroit, Michigan, USA, as emigrants when he was only two years old.  He left school in 1869 and worked for a company which made plumbing products.  The company ran into trouble in 1882 that led Buick and a partner to take it over. During this time, Buick began to show his leanings as an inventor. He produced many innovations including a lawn sprinkler, and a method for permanently coating cast iron and vitreous enamel. With the combination of Buick's innovation and his partner's sound business management the company became quite successful.

Ne Me Quitte Pas (Song)

Chansons / Songs

The French song "Ne me quitte pas" ("Don't leave me"), is a 1959 song written by Jacques Brel, a Belgian singer-songwriter. It has been included in the original French by many singers/artists and has been translated into English and many other languages. It is one of his most popular songs; another is "Quand on n'a que l'amour".



 
Below is a popular adaptation, with English lyrics by poet, singer-songwriter Rod McKuen, "If You Go Away." Other recordings of the song include: Shirley Bassey (1967), Frank Sinatra (1969), and Neil Diamond (1971). Rod McKuen sang it beautifully in his later years, here - "If you go away".



Video Credit:  
 
Ne me quitte pas (Jacques Brel) - [English subtitles].  YouTube, uploaded by RandomLectures. Accessed September 11, 2012.

Rod McKuen - If You Go Away. Youtube, uploaded by Scout4Me1. Accessed September 11, 2012. 

Resource:

Ne me quitte pas (Song). en.wikipedia.org.  Accessed September 11, 2012.


(c) 2012.  Updated November 7, 2021. Tel. Inspired Pen Web. All rights reserved.