Unformatted text preview: 6. Prove that any pair of lines that meet at an angle θ can be moved by a Euclidean isometry onto any other pair of lines that meet at an angle θ . For problems 7 – 8 , you may use both analytic and rulerandcompass methods. 7. Prove that if two rigid motions agree on two distinct points, then they agree everwhere on the line joining those two points. 8. Let τ v be a translation, and let R C,α be a rotation around a point C ∈ E 2 . (a) Describe, geometrically, the isometry f := τ v ◦ R C,α ◦ τ1 v . This is the unique map that makes the following diagram commute: E 2 R C,α / τ v ± E 2 τ v ± E 2 f / _ _ _ _ _ _ E 2 What do R C,α and τ v ◦ R C,α ◦ τ1 v have in common? (b) Express R C,α as a composition of translations and rotations around the origin. MthSc 481  Topics in Geometry and Topology  Spring 2012  M. Macauley...
View
Full Document
 Spring '12
 Staff
 Geometry, Topology, Euclidean geometry, Euclidean space, Euclidean isometry

Click to edit the document details