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
2 days ago
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
2 days ago
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
2 days ago
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
2 days ago
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
2 days ago
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
2 days ago