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Laboratory rotations are typically a part of first year graduate school (Ph.D.-oriented) in American universities, especially in the research-oriented areas like biology and chemistry where an incoming student is expected to work in 4 to 6 different laboratories (each is called a "rotation") for durations of about 6 to 8 weeks, before making a final decision regarding which group he or she ...
The manipulations of the Rubik's Cube form the Rubik's Cube group. The Rubik's Cube group (,) represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be ...
Station rotation: a rotation model in which for a given course or the subject, the student rotates on a fixed schedule or at teacher's discretion one online learning station to another which might be activities such as small group instruction, group projects, and individual tutoring. It differs from individual-rotation model.
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space under the operation of composition. [ 1 ] By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry ), and orientation ...
Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
The odd-dimensional rotation groups do not contain the central inversion and are simple groups. The even-dimensional rotation groups do contain the central inversion −I and have the group C 2 = {I, −I} as their centre. For even n ≥ 6, SO(n) is almost simple in that the factor group SO(n)/C 2 of SO(n) by its centre is a simple group.
Only irreducible groups have Coxeter numbers, but duoprismatic groups [p,2,p] can be doubled to p,2,p by adding a 2-fold gyration to the fundamental domain, and this gives an effective Coxeter number of 2p, for example the [4,2,4] and its full symmetry B 4, [4,3,3] group with Coxeter number 8.
The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of its ...