Read the equation
Each integer equals the sum of the preceding two. With the standard seeds, this gives 0, 1, 1, 2, 3, 5, 8, and subsequent Fibonacci numbers. The recurrence is the direct constructive definition behind the manuscript’s closed form and ratio limit.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| F_n | Current integer |
| F_n_minus_1 | Previous integer |
| F_n_minus_2 | Integer two positions earlier |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
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 $\golden$:
\begin{equation}
\lim_{n \to \infty} \frac{\fib{n}}{\fib{n-1}} = \golden
\end{equation}Exact original notation
\fib{n} = \fib{n-1} + \fib{n-2}