Reciprocal golden-ratio identity

Read the equation

Dividing φ²=φ+1 by φ gives 1/φ=φ−1. Both sides are approximately 0.618033988749895. A rounded value such as 0.618 represents this constant, not a universal threshold for a measured system.

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Original context

\begin{definition}[Golden Ratio]
\begin{equation}
\golden = \frac{1 + \sqrt{5}}{2} \approx 1.618033988749895
\end{equation}
with conjugate $\golden^{-1} = \golden - 1 \approx 0.618033988749895$.
\end{definition}

\begin{definition}[Fibonacci Sequence]
$\fib{0} = 0$, $\fib{1} = 1$, and $\fib{n} = \fib{n-1} + \fib{n-2}$ for $n \geq 2$.
\end{definition}

The ratio of consecutive Fibonacci numbers converges to $\golden$:

\golden^{-1} = \golden - 1 \approx 0.618033988749895

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