0
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
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Rene
JudyAdd your answer:
Earn +20 pts
In hyperbolic geometry how many lines are there parallel to a given line through a given point?
infinitely many
Lines that are in the same plane but are not parallel are called?
Intersecting lines.
The intersection of a plane and cone?
If it's parallel to the base, it's a circle. If it doesn't go through the base, it's an ellipse. If it's does, it's hyperbolic/parabolic.
What are lines in the same plane that never intersect?
parallel lines ( I think)
Does a plane contain at least three lines?
Yes- planes contain infinitely many points and every pair of points in plane determine a line in that plane, so every plane contains infinitely many lines.
On a hyperbolic plane lines are?
infinitely long
Can perpendicular lines be intersecting lines?
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.)
Can two lines intersects and be perpendicular?
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.)
What has the author Dorcas Flannery written?
Dorcas Flannery has written: 'Mapping of the hyperbolic sine from the Z plane to the W plane and comparison with the hyperbolic cosine'
Is it possible for two lines that are not in the same plane to be parallel?
No.When they are on different planes and they do not cross, they are called skew lines, they are not considered parallel. When they ARE parallel, it means that they do not cross and they both lie on ONE plane
What is parallel planes?
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
Is a circumference of a compact disk a real number or imaginary?
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.
What are trigonometric functions in mathematics?
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.
What are points and lines in a plane?
Points and lines on the same plane are coplanar.
In hyperbolic geometry how many lines are there parallel to a given line through a given point?
infinitely many
Can the lines of a plane intersect?
All non-parallel lines in a plane will intersect at some point in the plane.
What are Two lines are if they lie in the same plan and have no points in common?
If there are no common points but both lines lie n the same plane they are considered "coplanar points"
