![]() ![]() For example, fundamental ideas were laid out for a plane characterized by the quadratic form x 2 − y 2. The idea of a group of motions for special relativity has been advanced as Lorentzian motions. Furthermore, the manifold has constant curvature if and only if, for every pair of points and every isometry, there is a motion taking one point to the other for which the motion induces the isometry. When the underlying space is a Riemannian manifold, the group of motions is a Lie group. In the plane, a direct Euclidean motion is either a translation or a rotation, while in space every direct Euclidean motion may be expressed as a screw displacement according to Chasles' theorem. For example, the Euclidean group is noted for the normal subgroup of translations. This group of motions is noted for its properties. ![]() Given a geometry, the set of motions forms a group under composition of mappings. In differential geometry, a diffeomorphism is called a motion if it induces an isometry between the tangent space at a manifold point and the tangent space at the image of that point. Some geometers define motion in such a way that only direct motions are motions. Indirect, or improper motions are motions like reflections, glide reflections and Improper rotations that invert the orientation of a chiral shape. Motions can be divided into direct and indirect motions.ĭirect, proper or rigid motions are motions like translations and rotations that preserve the orientation of a chiral shape. In the latter case, hyperbolic motions provide an approach to the subject for beginners. More generally, the term motion is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry. ![]() For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. In geometry, a motion is an isometry of a metric space. Send us feedback about these examples.Transformation of a geometric space preserving structure A glide reflection is a type of Euclidean motion. These examples are programmatically compiled from various online sources to illustrate current usage of the word 'reflection.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Cheri Lucas Rowlands, Longreads, 21 Sep. 2023 These are poignant reflections and questions from a thoughtful writer. Stephania Taladrid, The New Yorker, 25 Sep. 2023 The media was-and still is-a reflection of society. Jean Guerrero, Los Angeles Times, 26 Sep. 2023 In emotionally raw and poignant scenes interwoven with useful reflections, Campoverdi explores the toll of this tension on her own psyche, including her experiences with panic disorder while working multiple jobs as a student at USC and later Harvard University. 2023 Netanyahu’s impressive endurance in office is, in part, a reflection of his enlarged base. 2023 Their immorality is not a reflection of their individual failings but a reflection of the infectious petri dish that nurtures their growth. 2023 Whether any particular type of machine learning is good or evil is ultimately a reflection of decisions made by people, not technology. 2023 Deep reflection and introspection define these individuals. Recent Examples on the Web The crash was partly a reflection of just how high the market had flown but also of less willingness among investors to finance stock purchases when rising borrowing costs made that much more expensive. ![]()
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