Euclid's Axiom (Noun)
Meaning
(mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry.
Classification
Nouns denoting cognitive processes and contents.
Examples
- Euclid's axiom was first questioned by mathematicians in the 19th century who began to develop non-Euclidean geometries.
- Mathematicians found it difficult to prove that the parallel postulate, one of Euclid's axioms, could be derived from the other four.
- The set of theorems and proofs developed from Euclid's axioms was eventually published as the 'Elements', a 13-book treatise.
- In order to rigorously develop geometry, Euclid's axioms had to be modified to avoid hidden assumptions and clarify certain terms.
- By abandoning one of Euclid's axioms, mathematicians were able to create entirely new and self-consistent systems of geometry.