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Unformatted text preview: until the line ` t overlays the x axis, then perform the ip j over the x axis, and nally rotate the disk so that ` t is returned to its original position. Thus j t D r t jr t , or j t r t D r t j . Therefore, we need only work out how to compute products involving the ip j and the rotations r t . Note that j applied to a point 2 4 cos .s/ sin .s/ 3 5 in the disk is 2 4 cos . s/ sin . s/ 3 5 , and r t applied to 2 4 cos .s/ sin .s/ 3 5 is 2 4 cos .s C t/ sin .s C t/ 3 5 : In the Exercises, you are asked to verify the following facts about the group D : 1. jr t D r t j , and j t D r 2t j D jr 2t . 2. All products in D can be computed using these relations....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

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