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Euclidean Geometry is based on the premise that through any point there is only one line that can be drawn parallel to another line. It is based on the geometry of the Plane.
There are basically two answers to your question:
(i) Through any point there are NO lines that can be drawn parallel to a given line (e.g. the geometry on the Earth's surface, where a line is defined as a great circle. (Elliptic Geometry)
(ii) Through any point, there is an INFINITE number of lines that can be drawn parallel of a given line. (I think this is referred to as Riemannian Geometry, but someone else needs to advise us on this)
Both of these are fascinating topics to study.
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Does the parallel postulate in Euclidean geometry work in spherical geometry?
No.
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.
What is ruler placement postulates?
The ruler placement postulate is the third postulate in a set of principles (postulates, axioms) adapted for use in high schools concerning plane geometry (Euclidean Geometry).
Does a line go on forever in both directions?
In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.In Euclidean geometry, yes.
What is a characteristic of non-euclidean geometry?
One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
