# Euler-Binet Formula/Corollary 1/Mistake

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## Source Work

1997: David Wells: *Curious and Interesting Numbers* (2nd ed.):

- The Dictionary
- $5$

## Mistake

*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*

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

## Correction

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 $1986$.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $5$