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1. Explain what is a reflection in the Poincaré Disk. 2. Show that a reflection in the Poincaré Disk sends points on one side of the line to the other side of the line, and keeps points on the line invariant. 3. Show that any point can be move to another point by two reflections. 4. Show that any two rays sharing the same endpoint can be transformed into each other by a reflection. 5. (Harder) Can we define the translation (as in R²) as a rigid motion in the Poincaré Disk? Explain your answer

1. Explain what is a reflection in the Poincaré Disk. 2. Show that a reflection in the Poincaré Disk sends points on one side of the line to the other side of the line, and keeps points on the line invariant. 3. Show that any point can be move to another point by two reflections. 4. Show that any two rays sharing the same endpoint can be transformed into each other by a reflection. 5. (Harder) Can we define the translation (as in R²) as a rigid motion in the Poincaré Disk? Explain your answer

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Rigid Motion in Poincaré Disk 1. Explain what is a reflection in the Poincaré Disk. 2. Show that a reflection in the Poincaré Disk sends points on one side of the line to the other side of the line, and keeps points on the line invariant. 3. Show that any point can be move to another point by two reflections. 4. Show that any two rays sharing the same endpoint can be transformed into each other by a reflection. 5. (Harder) Can we define the translation (as in R²) as a rigid motion in the Poincaré Disk? Explain your answer
Transcribed Image Text:Rigid Motion in Poincaré Disk 1. Explain what is a reflection in the Poincaré Disk. 2. Show that a reflection in the Poincaré Disk sends points on one side of the line to the other side of the line, and keeps points on the line invariant. 3. Show that any point can be move to another point by two reflections. 4. Show that any two rays sharing the same endpoint can be transformed into each other by a reflection. 5. (Harder) Can we define the translation (as in R²) as a rigid motion in the Poincaré Disk? Explain your answer
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