Answer:
1.What are elliptic geometries
2.what are hyperbolic geometries?
3.why was elliptic geometries developed
4.why was hyperbolic geometries developed?
Step-by-step explanation:
1.Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no lines parallel to a given line.
2 .Hyperbolic geometry, also called Lobachevskian Geometry, a non-Euclidean geometry that rejects the validity of Euclid's fifth, the “parallel,” postulate. ... In hyperbolic geometry, through a point not on a given line there are at least two lines parallel to the given line.
3.Felix Klein (1849–1925) modified the model by identifying each pair of antipodal points as a single point, see the Modified Riemann Sphere. With this model, the axiom that any two points determine a unique line is satisfied. Often an elliptic geometry that satisfies this axiom is called a single elliptic geometry.
4.The complete system of hyperbolic geometry was published by Lobachevsky in 1829/1830, while Bolyai discovered it independently and published in 1832.
hope this helps
The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.
The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.
These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.
The key fact that makes elliptic and hyperbolic geometries different from Euclidean geometry is the consideration of curvature in spaces.
In this case, Euclidean geometry considers only spaces with no curvatures, whereas elliptic geometry considers spaces with a constant negative curvature and hyperbolic geometry makes with spaces with a constant positive curvature.
The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.
The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.
These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.
We kindly invite to check this question on non-Euclidean geometry: https://brainly.com/question/16972917
