Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
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.
System context
Pythagorean theoremis aTheoremEstablished
Pythagorean theorem is a kind of theorem.
Mechanism: The Pythagorean theorem is a proven result: in a right triangle, the square on the longest side equals the sum of the squares on the other two.
- 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.
Structural neighbourhood: 2 → 8 → 12 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
- 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.
Formula
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.
a, b— legsc— hypotenuse
Key dates
- c. 530 BCEFormalizationAttributed to Pythagoras; the relation was already known to Babylonian mathematicians. — MacTutor History of Mathematics Archive
Check yourself
A quick check against a common misconception. Nothing is scored — picking the tempting-but-wrong answer just flags an idea worth revisiting.
Which statement is correct?
The Pythagorean theorem works for any triangle.
It holds only for right-angled triangles. For other triangles you need the more general law of cosines.
Look for: Learner applies a² + b² = c² to a triangle with no right angle.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
In a right-angled triangle, the longest side (opposite the right angle) is linked to the other two by a rule: the square of the long side equals the squares of the two shorter sides added together — a² + b² = c².
For any right triangle, a² + b² = c², where c is the hypotenuse. It underlies the distance between two points in coordinate geometry and generalises to the length of vectors, making it one of the most reused results in all of mathematics.
- Connects 2 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
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence