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What is the minimum number of points any line contains?
In Euclidean geometry each line contains a minimum of an infinite number of points. In projective geometry, though, a line may have as few as two points.
What two points are collinear?
Any two points are always collinear, since you can draw a straight line passing through any two points.
What is elliptical geometry and examples?
Elliptical geometry is like Euclidean geometry except that the "fifth postulate" is denied. Elliptical geometry postulates that no two lines are parallel.One example: define a point as any line through the origin. Define a line as any plane through the origin. In this system, the first four postulates of Euclidean geometry hold; through two points, there is exactly one line that contains them (i.e.: given two lines through the origin, there is one plane that contains them) and so on. However, it is nottrue that given a line and a point not on the line that there is a parallel line through the point (that is, given a plane through the origin, and a line through the origin, not on the plane, there is no other plane through the origin that is parallel to the given plane).
Points all in one plane?
Two dimensional geometry.
Is it true that two points are always collinear?
Yes, two points are always collinear. You can draw a line through any two points.
