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