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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.
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What are two types of Non-Euclidean Geometries?
The 2 types of non-Euclidean geometries are hyperbolic geometry and ellptic geometry.
What are the names of two types of non-Euclidean geometries?
There are several: hyperbolic, elliptic and projective are three geometries.
What are the names of Non Euclidean Geometries?
There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.
What are the names of Non-Euclidean 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.
Can two given lines with no point in common exist in the same plane?
Yes. (The answer may be complicated somewhat in non-Euclidean geometries, but it's possible in Euclidean geometry if the lines are parallel).
Why hilbert axiom of parallelism assert the existence of only at most one parallel line'?
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.
Can two line segments be both intersecting and parallel?
Not in Euclidean geometry, but in other geometries such lines are possible.
Can a triangle can have two parellel sides?
A Plane triangle cannot have parallel sides. A triangle on a sphere, represented in Mercator projection may do so, but that still does not make it so, for that is in spherical geometry. And there are other geometries than Euclidean (plane). Hyperbolic Geometry and Elliptic Geometry are the names of another two. These geometries are consistent within themselves, but some of the theorems in Euclidean geometry have different answers in these alternate geometries.
Can line segments have two midpoints?
not in euclidean geometry (I don't know about non-euclidean).
How many different lines are determined by two points?
In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!
What does non Euclidean apply to in real life?
Non-Euclidean geometry is most practical when used for calculations in three dimensions, as opposed to only two. For example, planning the fastest route for an airplane or a ship to travel across the world requires non-Euclidean geometry, because the Earth is a sphere.
How many types of geometry do mathematicians study?
Mathematicians study various types of geometry, but the most common ones include Euclidean geometry, which studies flat, two-dimensional space, and three-dimensional space; and non-Euclidean geometry, which explores curved spaces such as spherical and hyperbolic geometries. Differential geometry is another branch that focuses on the study of curves and surfaces using calculus techniques, while algebraic geometry investigates geometric objects defined by algebraic equations. Finally, fractal geometry delves into the study of intricate, self-repeating geometric patterns.
