Rotational symmetries of the n-gon. (a) Recall the definition of the n-gon Gn, n >...
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Rotational symmetries of the n-gon. (a) Recall the definition of the n-gon Gn, n > 3, given earlier in this course. (b) Consider the collection R of all matrices of the form ro= cos(0) sin(0) sin(0) cos(0) O ER. > 100) = 669) ces, Show that the triple (R, o, I2 = with o denotes multiplications of matri- is a group. This group is called the group of rotations of the plane RP. (c) Consider the natural action of the group R on R2. Compute the subgroup Stabr(Gn). Rotational symmetries of the n-gon. (a) Recall the definition of the n-gon Gn, n > 3, given earlier in this course. (b) Consider the collection R of all matrices of the form ro= cos(0) sin(0) sin(0) cos(0) O ER. > 100) = 669) ces, Show that the triple (R, o, I2 = with o denotes multiplications of matri- is a group. This group is called the group of rotations of the plane RP. (c) Consider the natural action of the group R on R2. Compute the subgroup Stabr(Gn)
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