Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
At a glance
Key signals
0% cross fields · reaches 1 more
- Mathematics
- Geometry
- Explanation
- Examples
- Misconception
- Sourced relations 2
- 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
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
Golden ratiois aIrrational numberEstablished
golden ratio is a kind of irrational number.
Mechanism: The golden ratio is an irrational number (~1.618) that appears where a whole relates to its larger part as that part does to the smaller.
- 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: 2 of 2 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.
Structural neighbourhood: 2 → 6 → 16 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 2 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
2 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 Irrational number and Fibonacci sequence.
Formula
The ratio where the whole is to the larger part as the larger is to the smaller.
\varphi— golden ratio
Key dates
- c. 300 BCEFormalizationEuclid defines the “extreme and mean ratio” in the Elements. — 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?”
Recursion & self-similarity6 disciplines · 4 concepts
Concepts
shares a mental model
shares a mental model
shares a mental model
- Function compositionAlgebra
shares a mental model
Mental models at work here
- Connects 2 other ideas across 2 disciplines.
- Most of its connections are of the “Kind & structure” kind.
- It exercises 1 reusable thinking pattern.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence