I sense you're talking about the infinite disk, the hyperbolic disk or the Poincare disk. The limit of the circumference is infinite and a real number and is not actually part of the hyperbolic plane.
Points and lines on the same plane are coplanar.
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
Lines which are parallel. All other lines on the same plane eventually intersect.
An arc-hyperbolic function is an inverse hyperbolic function.
Hyperbolic geometry is a beautiful example of non-Euclidean geometry. One feature of Euclidean geometry is the parallel postulate. This says that give a line and a point not on that line, there is exactly one line going through the point which is parallel to the line. (That is to say, that does NOT intersect the line) This does not hold in the hyperbolic plane where we can have many lines through a point parallel to a line. But then we must wonder, what do lines look like in the hyperbolic plane? Lines in the hyperbolic plane will either appear as lines perpendicular to the edge of the half-plane or as circles whose centers lie on the edge of the half-plane
In Euclidean plane geometry, two lines which are perpendicular not only can but must intersect. (I believe the same is true for elliptic geometry and hyperbolic geometry.)
In Euclidean plane geometry, two lines which are perpendicular not only can but must intersect. (I believe the same is true for elliptic geometry and hyperbolic geometry.)
Dorcas Flannery has written: 'Mapping of the hyperbolic sine from the Z plane to the W plane and comparison with the hyperbolic cosine'
Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect
I sense you're talking about the infinite disk, the hyperbolic disk or the Poincare disk. The limit of the circumference is infinite and a real number and is not actually part of the hyperbolic plane.
The basic ones are: sine, cosine, tangent, cosecant, secant, cotangent; Less common ones are: arcsine, arccosine, arctangent, arccosecant, arcsecant, arccotangent; hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, hyperbolic cotangent; hyperbolic arcsine, hyperbolic arccosine, hyperbolic arctangent, hyperbolic arccosecant, hyperbolic arcsecant, hyperbolic arccotangent.
Points and lines on the same plane are coplanar.
infinitely many
All non-parallel lines in a plane will intersect at some point in the plane.
Two lines can lie in one plane. For example, parallel lines are lines that intersect and lie in the same plane.
Two lines that do not intersect on the same plane are Parallel lines.