Inversions are transformation that play a central role in visualizing the transfor- mations of non-Euclidean geometry. Suppose C is a circle with radius r> 0 and center zo E C. Inversion in the circle C, denoted ic sends a point z zo to the point z defined as follows: First, construct the ray from zo through 2. Then, let z be the unique point on this ray that satisfies the equation: |z-zo|-|z* - zo| = r². The point z is called the symmetric point to z with respect to C. 3.1 Find the expression of the inversion in the unit circle, i.e. that of is 3.2 What is the image of the unit circle under işı.
Inversions are transformation that play a central role in visualizing the transfor- mations of non-Euclidean geometry. Suppose C is a circle with radius r> 0 and center zo E C. Inversion in the circle C, denoted ic sends a point z zo to the point z defined as follows: First, construct the ray from zo through 2. Then, let z be the unique point on this ray that satisfies the equation: |z-zo|-|z* - zo| = r². The point z is called the symmetric point to z with respect to C. 3.1 Find the expression of the inversion in the unit circle, i.e. that of is 3.2 What is the image of the unit circle under işı.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Inversions are transformation that play a central role in visualizing the transfor-
mations of non-Euclidean geometry.
Suppose C is a circle with radius r> 0 and center zo E C. Inversion in the circle
C, denoted ic sends a point z zo to the point z" defined as follows: First,
construct the ray from zo through 2. Then, let z* be the unique point on this
ray that satisfies the equation:
|zzo|-|z* = 20 = r².
-
The point z is called the symmetric point to z with respect to C.
3.1 Find the expression of the inversion in the unit circle, i.e. that of igi
3.2 What is the image of the unit circle under işı.
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