s12_mthsc481_hw05

# s12_mthsc481_hw05 - Homework 5 | Due March 6(Tuesday 1 Read...

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Homework 5 | Due March 6 (Tuesday) 1 Read : Stahl Chapters 6.1, 6.2, 7.1, 7.2, 8.1, 8.2, 8.3. 1. Prove that if 0 < α < 2 π then there is a hyperbolic quadrilateral whose angles sum to α . 2. For a,b > 0, let R ( a,b ) be the Euclidean rectangle with corners (0 , 2), ( a, 2), (0 , 2 + b ), and ( a, 2 + b ). (a) Give a qualitative description of what R looks like to a resident of the hyperbolic plane. Speciﬁcally, which of its sides are hyperbolically straight or hyperbolically curved. If curved, in which direction? (b) For a given a,b > 0, let ha( R ( a,b )) denote the hyperbolic area of R ( a,b ), let L ( a,b ) be the hyperbolic length of the left side of R , and let B ( a,b ) be the hyperbolic length of the bottom side of R . Prove that lim a,b 0 + L ( a,b ) B ( a,b ) ha( R ( a,b )) = 1 . For the next two problems, consider a hyperbolic right triangle ABC with right angle at C , let α and β denote the angles at A and B , respectively, and let a , b , and c be the hyperbolic lengths of the sides opposite

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## This note was uploaded on 03/11/2012 for the course MTHSC 481 taught by Professor Staff during the Spring '12 term at Clemson.

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s12_mthsc481_hw05 - Homework 5 | Due March 6(Tuesday 1 Read...

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