non-euclidean

Meanings

• adjective

  Relating to or being a geometry that does not satisfy Euclid's axioms, especially a geometry in which the parallel postulate is not true.

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Variants

List of all variants of non-euclidean that leads to same result
non-euclidean

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Etymology

origin and the way in which meanings have changed throughout history.

Derived from the name of the ancient Greek mathematician Euclid and the Greek word for 'not' and 'true' or 'false'.

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Trivia

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1. Non-Euclidean geometry was first discovered by the mathematician János Bolyai and the mathematician Nicolai Ivanovich Lobachevsky independently in the late 1800s.

2. Albert Einstein's theory of general relativity is based on the principles of non-Euclidean geometry.

3. Non-Euclidean geometry has been used to model the universe according to some theories of physics.

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Related Concepts

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1. Euclidean geometry: A type of geometry that satisfies Euclid's axioms and is the geometry that is most commonly used in everyday life and in mathematics.

2. Hyperbolic geometry: A type of non-Euclidean geometry where the parallel postulate is replaced with the assumption that there exist infinitely many lines parallel to a given line that pass through a given point.

3. Elliptic geometry: A type of non-Euclidean geometry where the parallel postulate is replaced with the assumption that there exist no parallel lines through a given point.

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Culture

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Non-Euclidean geometry has been a significant area of research in mathematics since its discovery in the late 19th century. It has applications in physics, particularly in the theory of relativity.

How to Memorize "non-euclidean"

1. visualize
   

   - Imagine a plane where the parallel lines do not meet at infinity. This is a visual representation of hyperbolic geometry, a type of non-Euclidean geometry.

2. associate
   

   - Associate the term 'non-Euclidean' with 'geometry' and 'not Euclidean'. This will help you remember that it is a type of geometry that does not satisfy Euclid's axioms.

3. mnemonics
   

   - Use the mnemonic 'Nice guys finish last, but Euclid's axioms don't' to remember that non-Euclidean geometry is not Euclidean.

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