Golden Ratio History

The golden ratio is a never-ending number approximately equal to 1.618. It is calculated when a length is separated into two parts, and the value obtained by dividing the longer section by the shorter section (1.618…) is equal to the value obtained by dividing the entire length by the longer section.

While the exact history of its conception is still unknown, it is known to have been derived in ancient Greece, sometime around 400 BC. Euclid, a Greek mathematician often called the “Father of Geometry” recorded the first written definition of the golden ratio in his treatise Elements, in 300 BC. Since its inception it has been held to be the most aesthetically pleasing ratio in everything from art and architecture to music. Luca Pacioli, an Italian mathematician called the golden ration the “divine proportion” in his Divina Proportione in 1509 further spreading the idea of a perfect ratio across the globe. This is of note as while Pacioli was a mathematician by trade he was also immensely interested in art and began advocating the golden ratio’s application in art and the design of buildings, again allowing its idea to be rapidly spread. The golden ratio has been discovered in the design of many classic buildings such as: the Parthenon, the Great Mosque of Kairouan, and Naqsh-e Jahan Square. Several famous architects have used the golden ratio in their designs such as the famous Swiss architects Mario Botta and Le Corbusier.
The golden ratio has been used extensively in art, as in creating the frame of paintings, or even in the paintings themselves. Leonardo da Vinci's illustrations of polyhedra in De divina proportione (On the Divine Proportion) as well as his views that some bodily proportions portray the golden ratio has c...

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...studied and analyzed throughout the years. Learning about quadratic equations was a major component of our class and in computing the inverse of the golden ratio one must employ quadratic equations. The first calculation of the inverse of the golden ratio by a decimal fraction, stated as "approximately 0.6180340", was recorded in 1597 by Michael Maestlin of the University of Tübingen in a letter to his former student Johannes Kepler.
Overall one can clearly see the significance of the golden ratio and the profound effect it has had on humans. By clearly understanding the golden ratio, can better understand and logically theorize other sequences and important numbers, such as the Fibonacci Sequence. While by employing the golden ratio one might not achieve the “perfect proportion” they will at the very least gain knowledge of the golden ratio and the math behind it.