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Constructing a hyperbolic line through two given points. a. Given a point p in D, construct the point p* symmetric to p with respect to the unit circle (see Figure 3.2.18). (1) (4) (1) z0 (2) (2) (a) (b) Figure 3.2.18. Constructing the symmetric point (a) if z is inside the circle of inversion; (b) if z is outside the circle of inversion. in-context b. Suppose q is a second point in D. Construct the cline through p, q, and p*. Call this cline C. Explain why C intersects the unit circle at right angles. c. Consider the portion of cline C you constructed in part (b) that lies in D. This is the unique hyperbolic line through p and q. Mark the ideal points of this hyperbolic line.

Constructing a hyperbolic line through two given points. a. Given a point p in D, construct the point p* symmetric to p with respect to the unit circle (see Figure 3.2.18). (1) (4) (1) z0 (2) (2) (a) (b) Figure 3.2.18. Constructing the symmetric point (a) if z is inside the circle of inversion; (b) if z is outside the circle of inversion. in-context b. Suppose q is a second point in D. Construct the cline through p, q, and p*. Call this cline C. Explain why C intersects the unit circle at right angles. c. Consider the portion of cline C you constructed in part (b) that lies in D. This is the unique hyperbolic line through p and q. Mark the ideal points of this hyperbolic line.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 5AEXP
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Constructing a hyperbolic line through two given points. a. Given a point p in D, construct the point p* symmetric to p with respect to the unit circle (see Figure 3.2.18). (1) (4) (3) 20 (2) (a) (b) Figure 3.2.18. Constructing the symmetric point (a) if z is inside the circle of inversion; (b) if z is outside the circle of inversion. in-context b. Suppose q is a second point in ID. Construct the cline through p, q, and p*. Call this cline C. Explain why C'intersects the unit circle at right angles. c. Consider the portion of cline C you constructed in part (b) that lies in ID. This is the unique hyperbolic line through p and q. Mark the ideal points of this hyperbolic line.
Transcribed Image Text:Constructing a hyperbolic line through two given points. a. Given a point p in D, construct the point p* symmetric to p with respect to the unit circle (see Figure 3.2.18). (1) (4) (3) 20 (2) (a) (b) Figure 3.2.18. Constructing the symmetric point (a) if z is inside the circle of inversion; (b) if z is outside the circle of inversion. in-context b. Suppose q is a second point in ID. Construct the cline through p, q, and p*. Call this cline C. Explain why C'intersects the unit circle at right angles. c. Consider the portion of cline C you constructed in part (b) that lies in ID. This is the unique hyperbolic line through p and q. Mark the ideal points of this hyperbolic line.
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