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In graph Frontier
MathematicsArithmeticEstablished

Irrational number

In mathematics, the irrational numbers are all the real numbers that are not rational numbers; that is, irrational numbers are those that cannot be expressed as the ratio of two integers.

Irrational numberReal numberPiGolden ratioNumberRational numberNegative real numberAbsolute valueCircle

At a glance

Type
information
Disciplines 2
MathematicsArithmetic
Mental models 0
—
Role in the graph
Connector

Key signals

Cross-disciplinary reach
Disciplines
2
  • Mathematics
  • Arithmetic
Evidence & development

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.

System context

Irrational numberis aReal numberEstablished

Open Real number →

irrational number is a kind of real number.

Mechanism: An irrational number is a real number that cannot be written as a ratio of integers; its decimal runs forever without repeating.

Sources:
Golden ratiois aIrrational numberEstablished

Open Golden ratio →

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.

Sources:
Piis aIrrational numberEstablished

Open Pi →

pi is a kind of irrational number.

Mechanism: Pi is an irrational number: the ratio of a circle's circumference to its diameter, whose decimal never ends or repeats.

Sources:

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.

  • Structural neighbourhood: 3 → 10 → 18 concepts reachable within 3 hops.

    structural · Structural reach — being reachable is not the same as being understood.

  • All 3 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.

0%

cross-field
3 within-field, 0 cross-field

0 of 3 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation

Conditions

  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Mathematics

Through this lens it connects to Real number, Pi and Golden ratio.

Irrational number through the Mathematics lens →

Arithmetic

Through this lens it connects to Real number.

Irrational number through the Arithmetic lens →

Key dates

  1. c. 450 BCEDiscoveryThe Pythagoreans (attributed to Hippasus) discover incommensurable magnitudes — irrational numbers. — MacTutor History of Mathematics Archive

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

The scientific picture
  • Connects 3 other ideas across 2 disciplines.
  • Most of its connections are of the “Kind & structure” kind.

Derived from the graph’s real structure — observations, not a score.

Sources