Definition:Golden Mean/Historical Note
Historical Note on Golden Mean
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.
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.
- 1953: H.S.M. Coxeter: The Golden Section, Phyllotaxis, and Wythoft's Game (Scripta Math. Vol. 19: pp. 135 – 143)
- 1961: Martin Gardner: The Second Scientific American Book of Mathematical Puzzles and Diversions
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$
- 1992: George Markowsky: Misconceptions about the Golden Ratio (College Math. J. Vol. 23: pp. 2 – 19) www.jstor.org/stable/2686193
- 1995: Peter Schreiber: A Supplement to J. Shallit's Paper “Origins of the Analysis of the Euclidean Algorithm” (Hist. Math. Vol. 22: pp. 422 – 424)
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: golden section