Definition of non-Euclidean in English:

non-Euclidean

adjective nɒnjuːˈklɪdɪənˌnän yo͞oˈklidēən

Geometry

Denying or going beyond Euclidean principles in geometry, especially contravening the postulate that only one line through a given point can be parallel to a given line.
〔几何〕非欧几里得的
Example sentencesExamples
- In 1915, Albert Einstein found it more convenient, the conventionalist would say, to develop his theory of general relativity using non-Euclidean rather than Euclidean geometry.
- A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry.
- Beltrami in this 1868 paper did not set out to prove the consistency of non-Euclidean geometry or the independence of the Euclidean parallel postulate.
- By chapter two he is proving Pythagoras' theorem from first principles and introducing non-Euclidean geometry.
- It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well.

Definition of non-Euclidean in US English:

non-Euclidean

adjectiveˌnän yo͞oˈklidēən

Geometry

Denying or going beyond Euclidean principles in geometry, especially contravening the postulate that only one line through a given point can be parallel to a given line.
〔几何〕非欧几里得的
Example sentencesExamples
- By chapter two he is proving Pythagoras' theorem from first principles and introducing non-Euclidean geometry.
- A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry.
- It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well.
- Beltrami in this 1868 paper did not set out to prove the consistency of non-Euclidean geometry or the independence of the Euclidean parallel postulate.
- In 1915, Albert Einstein found it more convenient, the conventionalist would say, to develop his theory of general relativity using non-Euclidean rather than Euclidean geometry.

单词	non-Euclidean
释义	Definition of non-Euclidean in English: non-Euclidean adjective nɒnjuːˈklɪdɪənˌnän yo͞oˈklidēən Geometry Denying or going beyond Euclidean principles in geometry, especially contravening the postulate that only one line through a given point can be parallel to a given line. 〔几何〕非欧几里得的 Example sentencesExamples In 1915, Albert Einstein found it more convenient, the conventionalist would say, to develop his theory of general relativity using non-Euclidean rather than Euclidean geometry. A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry. Beltrami in this 1868 paper did not set out to prove the consistency of non-Euclidean geometry or the independence of the Euclidean parallel postulate. By chapter two he is proving Pythagoras' theorem from first principles and introducing non-Euclidean geometry. It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well. Definition of non-Euclidean in US English: non-Euclidean adjectiveˌnän yo͞oˈklidēən Geometry Denying or going beyond Euclidean principles in geometry, especially contravening the postulate that only one line through a given point can be parallel to a given line. 〔几何〕非欧几里得的 Example sentencesExamples By chapter two he is proving Pythagoras' theorem from first principles and introducing non-Euclidean geometry. A modern realist would say that what mathematicians hadn't realised is that, as well as Euclidean geometry, there also exists non-Euclidean geometry. It can be shown that if Euclidean geometry is internally consistent, then the alternative non-Euclidean geometries are consistent as well. Beltrami in this 1868 paper did not set out to prove the consistency of non-Euclidean geometry or the independence of the Euclidean parallel postulate. In 1915, Albert Einstein found it more convenient, the conventionalist would say, to develop his theory of general relativity using non-Euclidean rather than Euclidean geometry.
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