5. (a) Use the cosh distance formula to prove that the hyperbolic circle of hyperbolic radius p = In 3 and center C = (1,0) in the Poincaré disk has Euclidean equation 2 2 x +42 = 4 25 (b) Prove that every hyperbolic circle in the Poincaré disk is in fact a Euclidean circle.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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5. (a) Use the cosh distance formula to prove that the hyperbolic circle of hyperbolic radius
p = In 3 and center C = (1,0) in the Poincaré disk has Euclidean equation
2
2
x
+42
=
4
25
(b) Prove that every hyperbolic circle in the Poincaré disk is in fact a Euclidean circle.
Transcribed Image Text:5. (a) Use the cosh distance formula to prove that the hyperbolic circle of hyperbolic radius p = In 3 and center C = (1,0) in the Poincaré disk has Euclidean equation 2 2 x +42 = 4 25 (b) Prove that every hyperbolic circle in the Poincaré disk is in fact a Euclidean circle.
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