Square of Golden Mean equals One plus Golden Mean/Decimal Expansion

From ProofWiki
Jump to navigation Jump to search

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:

$\sqrt n = n - 1$