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A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is ...
Time-translation symmetry is the law that the laws of physics are unchanged (i.e. invariant) under such a transformation. Time-translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time-translation symmetry is closely connected, via Noether's theorem, to conservation of energy. [1]
With rotational symmetry of order two of the pattern on the tile we have p2 (more symmetry of the pattern on the tile does not change that, because of the arrangement of the tiles). The rectangle is a more convenient unit to consider as fundamental domain (or set of two of them) than a parallelogram consisting of part of a tile and part of ...
Reflection: The writer reflects on the issue (that is, the topic they are writing about) and considers how their own experience and points of view might influence their response. This helps the writer learn about themselves as well as contribute to a better final product that considers biases.
The Fifth Quarter (or 5th Quarter) is an addition to a whole normally divided into four parts, usually referring to post-game activities after an American or Australian rules football game, which each are divided into four timing quarters. It may refer to: The Fifth Quarter (short story), written in 1972 by Stephen King