Parallel Axiom (Noun)
Meaning
Only one line can be drawn through a point parallel to another line.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The parallel axiom is a fundamental concept in Euclidean geometry, stating that only one line can be drawn through a point parallel to another line.
- Euclid's fifth postulate, also known as the parallel axiom, has been widely studied and debated by mathematicians throughout history.
- In non-Euclidean geometries, the parallel axiom is either replaced or modified to accommodate different types of parallel lines.
- The parallel axiom is essential for proving many theorems in geometry, including the theorem that the sum of the interior angles of a triangle is 180 degrees.
- By assuming the parallel axiom, mathematicians can derive numerous results and theorems that are consistent with our everyday experience of space and geometry.