parallel axiom Sentence Examples
- Euclid's parallel axiom is a fundamental postulate in Euclidean geometry.
- The parallel axiom states that through a given point not on a given line, there exists only one line parallel to the given line.
- The parallel axiom is equivalent to the statement that the sum of the interior angles of a triangle is 180 degrees.
- Alternative geometries can be constructed by negating the parallel axiom.
- In hyperbolic geometry, the parallel axiom is replaced by the statement that there are infinitely many lines parallel to a given line through a given point.
- In elliptic geometry, the parallel axiom is replaced by the statement that there are no lines parallel to a given line through a given point.
- The parallel axiom has been the subject of much debate and research throughout history.
- The discovery of non-Euclidean geometries in the 19th century challenged the traditional understanding of the parallel axiom.
- The parallel axiom plays a crucial role in the development of modern physics and cosmology.
- The search for a proof of the parallel axiom from the other axioms of Euclidean geometry has been a major problem in mathematics.
parallel axiom Meaning
Wordnet
parallel axiom (n)
only one line can be drawn through a point parallel to another line
Synonyms & Antonyms of parallel axiom
No Synonyms and anytonyms found
FAQs About the word parallel axiom
only one line can be drawn through a point parallel to another line
No synonyms found.
No antonyms found.
Euclid's parallel axiom is a fundamental postulate in Euclidean geometry.
The parallel axiom states that through a given point not on a given line, there exists only one line parallel to the given line.
The parallel axiom is equivalent to the statement that the sum of the interior angles of a triangle is 180 degrees.
Alternative geometries can be constructed by negating the parallel axiom.
