Euler-Binet Formula/Corollary 1/Mistake

Source Work

The Dictionary

$5$

There is another version of this formula, which is simpler to use in practice. Because

$\dfrac 1 {\sqrt 5} \paren {\dfrac {1 + \sqrt 5} 2}^n$

is only $0 \cdotp 618 \ldots$ when $n = 1$ and rapidly becomes very small indeed, $F_n$ is actually the nearest integer to

$\paren {\dfrac {\sqrt 5 - 1} 2}^n$

The expressions are the wrong way round.

The section ought to read:

There is another version of this formula, which is simpler to use in practice. Because

$\paren {\dfrac {\sqrt 5 - 1} 2}^n$

is only $0 \cdotp 618 \ldots$ when $n = 1$ and rapidly becomes very small indeed, $F_n$ is actually the nearest integer to

$\dfrac 1 {\sqrt 5} \paren {\dfrac {1 + \sqrt 5} 2}^n$

Interestingly and oddly, this is correct in the first edition of Curious and Interesting Numbers of $1986$.