Definition:Golden Mean/Definition 1

Definition

Let a line segment $AB$ be divided at $C$ such that:

$AB : AC = AC : BC$

Then the golden mean $\phi$ is defined as:

$\phi := \dfrac {AB} {AC}$

Decimal Expansion

The decimal expansion of the golden mean starts:

$\phi \approx 1 \cdotp 61803 \, 39887 \, 49894 \, 84820 \, 45868 \, 34365 \, 63811 \, 77203 \, 09179 \, 80576 \ldots$

Also see

• Equivalence of Definitions of Golden Mean

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): golden section
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: The golden mean