Thinking·OS

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Explore the knowledge graph

Absolute value applies to Real number. Activate to inspect this relation.Birch–Swinnerton-Dyer conjecture applies to Prime number. Activate to inspect this relation.Circle depends on Pi. Activate to inspect this relation.Circumference depends on Pi. Activate to inspect this relation.Coefficient is a Number. Activate to inspect this relation.Coefficient is part of Polynomial. Activate to inspect this relation.Divisibility applies to Integer. Activate to inspect this relation.Divisor applies to Integer. Activate to inspect this relation.Fraction is a Rational number. Activate to inspect this relation.Fundamental theorem of arithmetic depends on Divisibility. Activate to inspect this relation.Fundamental theorem of arithmetic depends on Prime number. Activate to inspect this relation.Golden ratio emerges from Fibonacci sequence. Activate to inspect this relation.Golden ratio is a Irrational number. Activate to inspect this relation.Integer is a Rational number. Activate to inspect this relation.Irrational number is a Real number. Activate to inspect this relation.Modular arithmetic applies to Divisibility. Activate to inspect this relation.Natural number is a Integer. Activate to inspect this relation.Negative real number is a Real number. Activate to inspect this relation.Pi is a Irrational number. Activate to inspect this relation.Prime number depends on Divisor. Activate to inspect this relation.Prime number is a Natural number. Activate to inspect this relation.Rational number is a Real number. Activate to inspect this relation.Real number is a Number. Activate to inspect this relation.Rational numberReal numberFractionIntegerNumberIrrational numberNegative real numberAbsolute valueNatural numberDivisibilityDivisorCoefficientGolden ratioPiPrime numberFundamental theorem of arithmeticModular arithmeticPolynomialFibonacci sequenceCircleCircumferenceBirch–Swinnerton-Dyer conjecture
Relationship types

172 concepts viewed through this lens. Bridge concepts connect this view to Acoustics, Actuarial Science, Agriculture, Algorithms….

Legend
  • Focused concept
  • Connected concept
  • Bridge concept (just outside the lens)
  • Arrow points from cause / source to effect / target
  • A line with no arrow is a two-way relationship
  • Node colour marks the concept’s primary discipline
22 concepts23 relationships5 disciplines4 relation families

Rational number

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At a glance

In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠⁠ of two integers, a numerator p and a nonzero denominator q.

Disciplines
Mathematics · Arithmetic
Role in the graph
Connector
Relationships
3 · 1 relation families

What am I looking at?

In this lens (172)

Bridge concepts (186)

Just outside the lens — they connect it to other context.

  • Rate of change5
    Calculus, Economics, Physics · connects to Differential equation, Integral, Limit…
  • Enumerative counting4
    Combinatorics · connects to Combination, Generating function, Permutation…
  • Graph data structure4
    Computer Science, Data Structures · connects to Connectivity, Edge, Shortest path…
  • Machine learning3
    Artificial Intelligence, Computer Science, Machine Learning, Statistics · connects to Algorithm, Pattern, Probability
  • Optimization3
    Business, Economics, Engineering, Mathematical Modelling, Optimization, Systems Engineering · connects to Inequality, Linear programming, Mathematical model

Insights from this view

Structural observations about the concepts shown here — descriptions of this graph, not claims about the world.

  • This view connects 5 disciplines: Algebra, Arithmetic, Geometry, Mathematics, Number Theory.
  • Rational number is a bridge concept — viewed here through Arithmetic, Mathematics.
  • The connections here span 4 relation families.
  • Recursion explains 2 concepts in this view (Geometry, Mathematics).

Relationships as a list

The focused concept’s relationships. Pick another concept in the graph above to update this list.

Explore through a different lens

A lens is a deterministic projection of the graph. Pick a discipline, thinking pattern or journey to reframe the whole view.

By discipline

ChemistryBiologyPhysicsMathematicsComputer ScienceGeologyMineralogyEconomics

By thinking pattern

Bayesian updatingCause and effectCompoundingConservationConstraintsDefense in depthDiffusion & spreadEmergenceEnergy transformationEntropy & irreversibilityEquilibriumFeedback loopIncentivesInformationLevels & hierarchyModularityNetworksOptimizationOscillationProbabilityRecursion & self-similarityScaleSignal vs noiseSource–pathway–receptorStocks and flowsSymmetry & invarianceThresholds & tipping pointsTrade-offsTriangulationVariation & selectionWaves

By journey

From a Leaf to the ClimateWhy Music Moves UsHow Machines LearnReasoning about a Leaf and the Climate

Concept collections

Concept collections are curated lenses onto the fabric — themed sets of ideas that recur across disciplines. They are not journeys; they are a way to read the graph.

About this view

What this is

Start from one concept and expand outward. The view never shows everything at once — click a node to refocus, filter by relationship type, or switch to an accessible list.

One fabric

3750 concepts and 5051 typed relations form one connected component — no isolated silo.

How to read it

Focus a concept, or apply a lens (discipline, mental model, journey) to see only the threads that matter.