## The Golden Ratio – History

While technically the golden ratio has always existed? in mathematics and physically although it is unclear when it was first discovered. The term pops up in different periods of history, which would explain why the golden ratio has many names (The Divine Proportion, the Golden Rectangle, the Golden Mean… etc.)

Historians of mathematics suggest that the Golden Ratio was first understood and used as early as Egyptian times in ancient mathematicians. The ratio subsequently appears in Geometry within the design of the Pyramids. As Mario Livio points out in his book “The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number”, the Golden Ratio has influenced the work of “some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose. All have contemplated this simple ratio and its properties.”

“The fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.”

Greeks

The use of the Golden Ratio in different civilisations has been the subject of much dispute. Many would argue that the Greeks were one of the first civilisations to discover the golden ratio and to use it for practical means including the constructions of buildings. They experimented with the use of the ratio within triangles, rectangles. The Greek sculptor Phidias was said to have influenced the design of the Parthenon using has the Golden Ratio throughout this structure.

However, some people deny that the Greeks held an association with golden ratio. One critic, Keith Devlin says, “Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation. The one thing we know for sure is that Euclid, in his famous textbook Elements, written around 300 BC, showed how to calculate its value.”

The Renaissance

The Renaissance cultural movement brought a mass of artistic revolution. This “shift” in art was the transitional period from the end of the middle ages and the start of the modern age. The timescale for this movement is believed to have commenced from the 14th century in Italy.
The renaissance artists at that time used the golden ratio abundantly within their paintings and sculptures. However they did not call it the Golden Ratio, they called it “the Divine Proportion” – reflecting its God like properties.

The words “Divine Proportion” originated from a publication by Luca Pacioli in 1509 entitled “De Divina Proporione” which Leonardo Da Vinci provided illustrations and drawings for.
Da Vinci, used it to define the proportions within his painting of “The Last Supper”. This contains a golden ratio in several places, appearing in both the ceiling and the position where the people sit.

Another example can be found in the Da Vinci’s painting the Mona Lisa, which is full of golden rectangles of 1.618.

Mona Lisa’s face uses a rectangular structure based on the Golden Ratio. According to the ratio of the width of her forehead compared to the length from the top of her head to her chin. This may not be a big surprise to some and Leonardo was, after all, a mathematician. But again, like the Greeks, speculation is rife about whether the golden ratio directly influenced the work of De Vinci. Mario Livio himself points out that Da Vinci’s Mona Lisa “has been the subject of so many volumes of contradicting scholarly and popular speculations that it virtually impossible to reach any unambiguous conclusions” with respect to the golden ratio.

Either way – for some interactive fun time have a play with the Mona Lisa Applet.