Examples of Golden Ratio

Examples of Golden Ratio can be found in nature and in manmade artifacts as well as buildings and even music.

The Golden Ratio is also called the Divine Ratio because it’s an infinite number that can’t be used as a whole number or fraction. The number is written as 1.62, an abbreviation of 1.618033989. This numeric value is known as Phi.

You can find the Divine Ratio in all of nature. Mathemeticians, musicians and artists also use the Golden Ratio. Because of its unique properties, many beleive the Golden Ratio, Golden Rectangle (also known as the Golden Proportions) and the Golden Triangle to be divine. When used in architecture, the building is said to be created by using "sacred architecture".

The Fibonacci Sequence or Series has a relationship to the Golden Ratio. The Fibonacci Series shows up in the number of leaves on a plant and the number of petals on a flower. A Fibonacci spiral, which is found in nature, is always part of a Golden Rectangle with a Golden Ratio.

The Fibonacci Series math is simple. Simply add the last two numbers together to get the next number in the series. The sequence begins with 0 and 1.

Fibonacci Series Example: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 and so forth.

The Fibonacci's relationship to the Golden Ratio is realized when it's added forward, further and further. The more you add the series, the closer you get to the Golden Ratio.

To create a Golden Rectangle with the Fibonacci Sequence, you’ll start with a square, the same way you would when creating a Golden Rectangle. You’ll need to add another square to create a rectangle. Next time you'll add one and two and the next time you'll add five squares to the existing three and so forth. You’ll continue to add squares and eventually form a Golden Rectangle.

You can find many exemplary instances of how the Golden Ratio is used around the world.

Phidias, the Greek sculptor, used the Golden Ratio in his work, especially when he began to work with the bands he sculpted just above the Parthenon columns. It's also important to note that the numeric value assigned to the Golden Ratio, Phi, was named in his honor.

If you measure the dimensions of the Parthenon's exterior, you’ll discover that it not only forms a Golden Rectangle, but that there are also many golden rectangles between the columns. The use of the Golden Ratio accounts for the genius and beauty of this example of sacred architecture.

The Golden Ratio, Golden Rectangle and Golden Triangle can all be found in the perfection of one of the seventh wonders of the world, the Great Pyramid of Giza. To find the Golden Ratio, you’ll need to half the square base of the pyramid and draw a vertical line up the center of the pyramid. When this is connected to an angled side of the pyramid, you can easily see how it forms Golden Triangle with a 1.62 ratio, the Golden Ratio.

You can find many examples of ancient to modern sacred architecture.

• Chartres Cathedral - Centre, France
• Notre Dame - Paris, France
• Porch of Maidens - Acropolis, Athens
• Taj Mahal - Agra, India
• United Nations Building - New York City, New York

You can find many examples by master artists who understood and used the Golden Ratio. Theses works of perfection were created by the use of Golden Rectangles (Golden Proportions or Sections) and Golden Triangles.

• Botticelli - Birth of Venus
• Leonardo Di Vinci - Mona Lisa, Vitruvian Man
• Michelangelo - Holy Family', David
• Raphael - Crucifixion
• Rembrandt - Self-Portrait
• Salvador Dali - The Sacrament of the Last Supper, The Persistence of Memory

Music is composed of numeric value and when the Golden Ratio is used to create a musical piece, it becomes a living example of math.

The Fiboncci Sequence is also prevalent in music:

• There are eight notes to a scale
• The third and fifth notes are the basis of all chords.
• The span (octave) of any note is 13 notes

The sequencing continues throughout a piece of music and becomes more complex as it reaches the Golden Ratio. A few of the composers who used the Golden Ratio and Fibonacci Sequencing in music pieces.

• Bach
• Beethoven
• Chopin
• Claude Debussy
• Liszt
• Ravel
• Schubert
• Wolfgang Mozart

Modern composer, Casey Mongoven, explores the Golden Ratio and Fibonacci Sequence in his music.

A Fibonacci spiral can be created by using the Golden Ratio. This is a phenomenon that’s found in nature. A plant's leaves grown so as many as possible can spiral up the stem. A new leave only forms after the one proceeding it has formed.

• Nautilus Seashell
• Spiral Cacti
• Spiral Galaxies
• Sunflowers

Some flowers that have flower petals that follow the Fibonacci Sequence:

• Three petals - Iris, lily, orchids, trillium,
• Five petals - Buttercups, geraniums, hibiscus, morning glory, nasturtium
• Eight petals - Delphiniums
• 13 petals - Certain varieties of daisies, ragwort, marigold

Depending on the tree species, you can also see the Golden Ratio at work within a Fibonacci number series in pinecones. You can find a series of eight spirals on one side of the pinecone with 13 spirals on the other. Another pinecone pattern has five spirals on one side with eight on the other.

The unique pattern of a pineapple is composed of diagonal shapes with eight moving in one direction and 13 in the opposite direction.

The human body and facial construction are considered beautiful the closer the features and bone structures are to the Golden Ratio.

One of the most amazing examples of Golden Ratio is found withint the human DNA structure.

• Monuments with the Golden Ratio
• Yin Yang Pictures
• Yin Yang Art

• Yin Yang Dragons
• Tiger and Dragon Ying Yang
• Applications How to Place Feng Shui Elephant
• Chinese Dragon Clip Art
• Ying Yang Suns

• Category:Feng Shui Tips
• Main Page