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In graph Frontier
MathematicsGeometryEstablished

Pi

The number π is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.

PiCircleIrrational numberCircumferenceSymmetryAreaReal numberGolden ratioPerimeter

At a glance

Type
patterns
Disciplines 2
MathematicsGeometry
Mental models 0
—
Role in the graph
Connector

Key signals

Cross-disciplinary reach
Disciplines
2
  • Mathematics
  • Geometry
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.

Enables · leads to

Circledepends onPiEstablished

Open Circle →

circle depends on pi.

Mechanism: Every circle's circumference divided by its diameter equals pi — the same constant for all circles.

Sources:
Circumferencedepends onPiEstablished

Open Circumference →

circumference depends on pi.

Mechanism: A circle's circumference depends on pi: it equals pi times the diameter, the constant ratio that holds for every circle.

Sources:

System context

Piis aIrrational numberEstablished

Open Irrational number →

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 → 8 → 16 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

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

CircleCircumferencePi◀ builds onenables ▶

What builds on this

2 concepts build on this directly, 2 in total, across 2 disciplines.

GeometryMathematics

Structural downstream reach along dependency edges — not a claim of historical necessity.

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 Irrational number, Circle and Circumference.

Pi through the Mathematics lens →

Geometry

Through this lens it connects to Circle and Circumference.

Pi through the Geometry lens →

Key dates

  1. c. 250 BCEFormalizationArchimedes bounds π between 3 10/71 and 3 1/7 in Measurement of a Circle. — 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 “Dependency” kind.

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

Sources