Unformatted text preview: until the line ` t overlays the x –axis, then perform the ﬂip j over the x – axis, and ﬁnally 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 ﬂip j and the rotations r t . Note that j applied to a point 2 4 ² cos .s/ ² sin .s/ 3 5 in the disk is 2 4 ² cos . ± s/ ² sin . ± s/ 3 5 , and r t applied to 2 4 ² cos .s/ ² sin .s/ 3 5 is 2 4 ² cos .s C t/ ² 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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 Fall '08
 EVERAGE
 Algebra, disk, COS.

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