Calculate the shortest distance from the vertex of a Schweikart triangle to the opposite side
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Let ∆ be an ideal triangle in the hyperbolic plane H2 with one right angle
at P and two other vertices at infinity. In other words, suppose you are given two
hyperbolic lines a and b intersecting at a right angle at P, and a third hyperbolic line c
ultraparallel to both a and b. The distance of c to P is defined as the minimum distance
of a point on c to the point P. Calculate this distance.
Can anyone give me a hint on how to tackle the problem?
hyperbolic-geometry
asked Nov 16 at 5:21
David Kendell
42
add a comment |
up vote
-1
down vote
favorite
Let ∆ be an ideal triangle in the hyperbolic plane H2 with one right angle
at P and two other vertices at infinity. In other words, suppose you are given two
hyperbolic lines a and b intersecting at a right angle at P, and a third hyperbolic line c
ultraparallel to both a and b. The distance of c to P is defined as the minimum distance
of a point on c to the point P. Calculate this distance.
Can anyone give me a hint on how to tackle the problem?
hyperbolic-geometry
asked Nov 16 at 5:21
David Kendell
42
How about drawing the setup in the Poincare model?
– Lord Shark the Unknown
Nov 16 at 5:30
The problem is that I'm sure the shortest distance is the Euclidean distance, but i don't know how that would look on the disk.
– David Kendell
Nov 16 at 5:44
Distance in the Poincare model is almost never equal to Euclidean distance. Do you know the form of the metric in any model, such as the Poincare disc model?
– Lee Mosher
Nov 16 at 17:50
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let ∆ be an ideal triangle in the hyperbolic plane H2 with one right angle
at P and two other vertices at infinity. In other words, suppose you are given two
hyperbolic lines a and b intersecting at a right angle at P, and a third hyperbolic line c
ultraparallel to both a and b. The distance of c to P is defined as the minimum distance
of a point on c to the point P. Calculate this distance.
Can anyone give me a hint on how to tackle the problem?
hyperbolic-geometry
asked Nov 16 at 5:21
David Kendell
42
Let ∆ be an ideal triangle in the hyperbolic plane H2 with one right angle
at P and two other vertices at infinity. In other words, suppose you are given two
hyperbolic lines a and b intersecting at a right angle at P, and a third hyperbolic line c
ultraparallel to both a and b. The distance of c to P is defined as the minimum distance
of a point on c to the point P. Calculate this distance.
Can anyone give me a hint on how to tackle the problem?
hyperbolic-geometry
hyperbolic-geometry
asked Nov 16 at 5:21
David Kendell
42
asked Nov 16 at 5:21
David Kendell
42
edited Nov 16 at 5:26
asked Nov 16 at 5:21
David Kendell
42
asked Nov 16 at 5:21
David Kendell
42
asked Nov 16 at 5:21
David Kendell
42
42
How about drawing the setup in the Poincare model?
– Lord Shark the Unknown
Nov 16 at 5:30
The problem is that I'm sure the shortest distance is the Euclidean distance, but i don't know how that would look on the disk.
– David Kendell
Nov 16 at 5:44
Distance in the Poincare model is almost never equal to Euclidean distance. Do you know the form of the metric in any model, such as the Poincare disc model?
– Lee Mosher
Nov 16 at 17:50
add a comment |
How about drawing the setup in the Poincare model?
– Lord Shark the Unknown
Nov 16 at 5:30
The problem is that I'm sure the shortest distance is the Euclidean distance, but i don't know how that would look on the disk.
– David Kendell
Nov 16 at 5:44
Distance in the Poincare model is almost never equal to Euclidean distance. Do you know the form of the metric in any model, such as the Poincare disc model?
– Lee Mosher
Nov 16 at 17:50
How about drawing the setup in the Poincare model?
– Lord Shark the Unknown
Nov 16 at 5:30
How about drawing the setup in the Poincare model?
– Lord Shark the Unknown
Nov 16 at 5:30
The problem is that I'm sure the shortest distance is the Euclidean distance, but i don't know how that would look on the disk.
– David Kendell
Nov 16 at 5:44
The problem is that I'm sure the shortest distance is the Euclidean distance, but i don't know how that would look on the disk.
– David Kendell
Nov 16 at 5:44
Distance in the Poincare model is almost never equal to Euclidean distance. Do you know the form of the metric in any model, such as the Poincare disc model?
– Lee Mosher
Nov 16 at 17:50
Distance in the Poincare model is almost never equal to Euclidean distance. Do you know the form of the metric in any model, such as the Poincare disc model?
– Lee Mosher
Nov 16 at 17:50
add a comment |
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How about drawing the setup in the Poincare model?
– Lord Shark the Unknown
Nov 16 at 5:30
The problem is that I'm sure the shortest distance is the Euclidean distance, but i don't know how that would look on the disk.
– David Kendell
Nov 16 at 5:44
Distance in the Poincare model is almost never equal to Euclidean distance. Do you know the form of the metric in any model, such as the Poincare disc model?
– Lee Mosher
Nov 16 at 17:50