What Is the Golden Ratio

Have you ever asked yourself the question "What is the Golden Ratio?" If you have, you are wondering about something that is mathematically explained and found all around you in the arts and sciences, nature and life itself.

More examples of the Golden Ratio

An example of an irrational number in mathematics, the Golden Ratio is a constant that represents a ratio of two quantities and how they relate to one another. The mathematical value of the Golden Ratio is an infinite number. Although mathematicians have actually carried the value of the Golden Ratio to 100,000,000,000 places, it is generally expressed as 1.618 and is known as Phi.

There are three ways that Phi can be derived:

• Using the Fibonacci series of numbers
• Using geometry
• Using mathematics

To many people the mathematical explanation of the Golden Ratio may seem complicated and confusing. However, it is really not necessary to understand the mathematical workings of the Golden Ratio to appreciate that Phi appears in almost every aspect of life and the universe, from the DNA that exists in the human body to the far reaches of outer space.

No one knows for certain exactly when the Golden Ratio was first discovered. Many believe that throughout history different ancient peoples discovered it, but may have called it by different names. Examples of the Golden Ratio and its application throughout history include:

• The Egyptians in the design of the pyramids as early as 2575 B.C.
• The Greeks in the design and proportions used in building the Parthenon from 448-432 B.C.
• Ancient Greek artists such as Phidias (500-432 B.C.) and philosophers including Plato (428-347 B.C.) studied and used the golden ratio in their works
• In his thirteen volume work Elements, the mathematician Euclid, referred to a dividing line at the point of 0.6180399. He explained it as the way to divide a line in the extreme and mean ratio. Euclid wrote Elements in approximately 300 B.C.
• The Fibonacci Series was discovered in 1200 A.D.
• In 1509 A.D. Leonardo Da Vinci illustrated a dissertation called De Divina Proportion or The Divine Proportion. The work includes Da Vinci’s drawings of the five Platonic Solids. Da Vinci referred to the Golden Ratio as Section Aurea or Golden Section.
• Known as the Divine Proportion by Renaissance artists, it gave their work exquisite balance and beauty. Excellent examples are The Last Supper and The Mona Lisa by Leonardo Da Vinci.
• In the early 1600's Johannes Kepler discovered that the elliptical orbits of the planets as they circled the sun and referred to the Divine Proportion in his explanation.
• It was not until the 1900's that the term Phi was used for the Golden Ratio.

• Golden Mean
• Golden Section
• Golden Number
• Golden Proportion
• Golden Cut
• Extreme Mean and Ratio
• Mean of Phidias
• Divine Section
• Medial Section
• Divine Proportion
• Phi

The Golden Ratio is found in many different aspects of nature. The following are several examples:

• The seed heads of sunflowers, daisies and many other types of flowers
• Pine cones
• Pineapples
• A moth
• A nautilus shell
• An ant

Examples of the Golden Ratio in architecture include:

• The CN Tower in Toronto was built from 1973-1976
• The Unite Nation Building in New York City was built from 1947-1953
• The Taj Mahal constructed in the 1500's in India
• Notre Dame in Paris built in 1100's

Phi is found in many aspects of life and the universe. The following are several additional examples:

• The human body
• DNA spirals
• A human embryo
• Teeth
• Penrose tiling
• The shape of the universe
• Honeybees
• The face of a tiger
• Phi mandalas

• The Golden Number
• Wolfram Math World
• The Golden Section by Hans Walser is available from Amazon

The simple answer to the question what is the Golden Ratio? is that it is a number. But it is a number that has great significance and importance. It is a number that connects and interconnects almost everything in the universe.

• 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

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