Fibonacci sequence
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it.
At a glance
Key signals
0% cross fields · reaches 7 more
- Mathematics
- Explanation
- Examples
- Misconception
- Sourced relations 3
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Foundations · builds on
Fibonacci sequencedepends onRecursionEstablished
Fibonacci sequence depends on recursion.
Mechanism: The Fibonacci sequence is defined by recursion: each term is the sum of the two before it, so the rule refers back to itself.
- Wikipedia (English & German editions) verifiedmoderate evidence
Enables · leads to
Golden ratioemerges fromFibonacci sequenceEstablished
golden ratio emerges from Fibonacci sequence.
Mechanism: Divide each Fibonacci number by the one before it and the ratios close in on the golden ratio, about 1.618.
- Wikipedia (English & German editions) verifiedmoderate evidence
System context
Fibonacci sequenceis aSequenceEstablished
Fibonacci sequence is a kind of Sequence.
Mechanism: The Fibonacci sequence starts 1, 1, 2, 3, 5, 8… with each term the sum of the two before it.
- Wikipedia (English & German editions) verifiedmoderate evidence
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: 3 of 3 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Exercises 2 annotated mental models — a concept that connects several thinking patterns.
curated · Curated annotations, not a derived measure.
Structural neighbourhood: 3 → 8 → 48 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
cross-field
3 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
Conditions
- Its dependency reading rests on 1 foundation relation. structural
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Sequence, Recursion and Golden ratio.
Formula
Each term is the sum of the two preceding ones.
F(n)— n-th Fibonacci number
Key dates
- 1202PublicationFibonacci introduces the sequence to Europe in Liber Abaci (also known earlier to Indian mathematicians). — MacTutor History of Mathematics Archive
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Compounding23 disciplines · 17 concepts
Recursion & self-similarity7 disciplines · 5 concepts
Concepts
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
Mental models at work here
Compounding
When each step's growth is added to the base so the next step grows too — producing accelerating, exponential change rather than a steady line.
Growth that feeds on itself starts slow and then surprises you.
Recursion & self-similarity
A thing defined in terms of smaller copies of itself — solve the small case and the same rule builds the whole, often looking similar at every scale.
Ask: can I reduce this to a smaller version of the same problem, plus a base case to stop? Zoom into a fractal and you see the whole again.
- Connects 3 other ideas across 1 discipline.
- A cross-disciplinary bridge — its connections reach into 7 other fields.
- Most of its connections are of the “Kind & structure” kind.
- It exercises 2 reusable thinking patterns.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence
- Generalized Fibonacci Sequences Generated from a $k$--Fibonacci Sequence (2012) verified
- Fibonacci and Pascal Together Again: Pattern Exploration in the Fibonacci Sequence (1998) verified