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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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[Classical Geometries] How do you solve this question? Thank you

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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