Square of Golden Mean equals One plus Golden Mean/Decimal Expansion
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Decimal Expansion of Square of Golden Mean
The decimal expansion of $\phi^2$ is given as:
- $\phi^2 \approx 2 \cdotp 61803 \, 39887 \, 49894$
This sequence is A104457 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Thus the square of the golden mean is the unique number $n$ such that:
- $\sqrt n = n - 1$
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2 \cdotp 618 \, 033 \ldots$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2 \cdotp 61803 \, 3 \ldots$