Definition:Golden Mean/Historical Note

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Historical Note on Golden Mean

The Egyptians knew about the golden mean. It was referred to in the Rhind Papyrus as sacred.

The heights of the Great Pyramids of Gizeh are almost exactly $\phi$ of half the lengths of their bases.


It is believed that the Ancient Greeks used $\phi$ in their architecture, but there is no extant documentary evidence of this.

Surprisingly, they had no short term for this concept, merely referring to it as the section.


The Renaissance artists exploited it and called it the Divine Proportion.

Fra Luca Pacioli discussed it in his book De Divina Proportione.

The first occcurrence of the term sectio aurea ("golden section") was probably by Leonardo da Vinci.


Mark Barr coined the use of the uppercase Greek letter $\Phi$ (phi) for the golden mean, originating from the Greek artist Phidias, who was said to have used it as a basis for calculating proportions in his sculpture.

Its companion value $\dfrac 1 \Phi = \Phi - 1$ was given the lowercase version $\phi$ or $\varphi$.

However, this convention is far from universal, and the larger value $1 \cdot 618 \ldots$ is usually denoted $\phi$.


It is said to produce the most pleasing proportions, and as a consequence many artists have used this ratio in their works.


A famous (or infamous, depending on how much reading you have done around the subject) article by George Markowsky attempts to debunks a number of myths surrounding the number.


Sources