Pythagorean theorem (equations)

Ontological representation of a classic equation example

Theorem as knowledge

The canonical equations branch uses the Pythagorean theorem to show how a classical geometric statement can be represented as structured knowledge subjects: sides of a triangle, real-valued measures, equality relating squares, and links to proofs or presentation formats for the web and print.

Read together with Equations and [AlHe2020]; logical typing of arithmetic fragments may involve concrete domains [BaMc2003].

Modeling sketch

On taoke.de, the theorem appears with figure and formula layout; the mirror page summarizes the intent—encode hypotenuse and legs as measurable quantities, attach the equation node to geometric concepts, and separate statement from proof artifacts if your KB distinguishes them.

Source: taoke.de — Pythagoras theorem.

References

  1. [AlHe2020] Dean Allemang, Jim Hendler, Fabien Gandon, Semantic Web for the Working Ontologist - Effective Modeling in RDFS and OWL, Third Edition, ACM Books series, Nbr. 33 , 2020, ISBN: 978-1-4503-7614-3
  2. [BaMc2003] Franz Baader, Deborah L. McGuiness, Daniele Nardi, Peter F. Patel-Schneider (eds.), The Description Logic Handbook: Theory, Implementation and Applications, Cambridge University Press , 2003, ISBN: 978-0521781763, pp. 574