s12_mthsc481_hw04

s12_mthsc481_hw04 - Homework 4 | Due February 21 (Tuesday)...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 4 | Due February 21 (Tuesday) 1 Read : Stahl, Chapters 4.4., 5.1, 5.2, 5.3, 5.4. 1. Find the Euclidean center and radius of the circle that has hyperbolic center (5 , 4) and radius 3. 2. Prove that the hyperbolic circumference of a circle with hyperbolic radius R is 2 π sinh( R ). 3. Prove Proposition 5.1.4 in Stahl, that in hyperbolic geometry, every angle is congruent to an angle in standard position. Recall that in class we showed this for right angles, which was the hyperbolic analog of Euclid’s Postulate 4. 4. Let P be a point in H 2 , and let be a Euclidean line segment through P . Prove that there exists a unique hyperbolic geodesic g that passes through P and is tangent to . (In other words, prove that, given a point P and a unit vector v , there is a unique geodesic through P that leaves P in the direction of v .) Also, give an explicit construction/description of g , given , using either ruler-and-compass or analytic methods. 5. Exercise 5.2.6 in Stahl asks you to consider the hyperbolic analog of the Euclidean theorem
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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

Ask a homework question - tutors are online