Elliptic and Hyperbolic geometry.
The 2 types of non-Euclidean geometries are hyperbolic geometry and ellptic geometry.
There are several: hyperbolic, elliptic and projective are three geometries.
Answer The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and elliptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates but the parallel postulate, these are the two possible geometries.
fishsticks
There is a subtle distinction between Euclidean, Hilbert and Non-Euclidean planes. Euclidean planes are those that satisfy the 5 axioms, while Non-Euclidean planes do not satisfy the fifth postulate. This means that in Non-Euclidean planes, given a line and a point not on that line, then there are two (or more) lines that contain that point and are parallel to the original line. There are geometries where there must be exactly one line through that point and parallel to the original line and then there are also geometries where no such line contains that point and is parallel to the original line.Basically, the fifth postulate can be satisfied by multiple geometries.
The 2 types of non-Euclidean geometries are hyperbolic geometry and ellptic geometry.
Hyperbolic, elliptic, projective are three possible answers.
There are several: hyperbolic, elliptic and projective are three geometries.
There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.
Answer The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and elliptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates but the parallel postulate, these are the two possible geometries.
fishsticks
In Euclidean space, never. But they can in non-Euclidean geometries.
No. Non-Euclidean geometries usually start with the axiom that Euclid's parallel postulate is not true. This postulate can be shown to be equivalent to the statement that the internal angles of a traingle sum to 180 degrees. Thus, non-Euclidean geometries are based on the proposition that is equivalent to saying that the angles do not add up to 180 degrees.
In some non-Euclidean geometries the 3 angles of a triange will add up to less than 180 degrees. In other non-Euclidean geometries they will add up to more than 180 degrees.
Hyperbolic and elliptic geometries are both non-Euclidean. The non-Euclidean idea is the approximate synonym to non-linear implying curvature between expectation and result. In applying it to cyclical geometries, the two options are hyperbolic which is circular and parabolic which is actually half of an elliptical trajectory. A familiar idea is the hyperbolic paraboloid or saddle shape. In this respect the ellipse is the syllogistic resultant between the hyperbolic and the parabolic: { ( hyp i [ ell 8 ) par b ] }. The contemporary difference between Cartesian linear and Ideal nonlinear (such as quantum relativity) is the idea that the metric curves while the empiricism converges it so that the estimate is approximate rather than deterministic and the resultant either improves or adjusts cybernetically.
plastic
There is a subtle distinction between Euclidean, Hilbert and Non-Euclidean planes. Euclidean planes are those that satisfy the 5 axioms, while Non-Euclidean planes do not satisfy the fifth postulate. This means that in Non-Euclidean planes, given a line and a point not on that line, then there are two (or more) lines that contain that point and are parallel to the original line. There are geometries where there must be exactly one line through that point and parallel to the original line and then there are also geometries where no such line contains that point and is parallel to the original line.Basically, the fifth postulate can be satisfied by multiple geometries.