parallel axiom Sentence Examples

  1. Euclid's parallel axiom is a fundamental postulate in Euclidean geometry.
  2. The parallel axiom states that through a given point not on a given line, there exists only one line parallel to the given line.
  3. The parallel axiom is equivalent to the statement that the sum of the interior angles of a triangle is 180 degrees.
  4. Alternative geometries can be constructed by negating the parallel axiom.
  5. 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.
  6. 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.
  7. The parallel axiom has been the subject of much debate and research throughout history.
  8. The discovery of non-Euclidean geometries in the 19th century challenged the traditional understanding of the parallel axiom.
  9. The parallel axiom plays a crucial role in the development of modern physics and cosmology.
  10. 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

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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.