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  2. Translation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Translation_(geometry)

    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 ...

  3. Transformation geometry - Wikipedia

    en.wikipedia.org/wiki/Transformation_geometry

    In mathematics, transformation geometry (or transformational geometry) is the name of a mathematical and pedagogic take on the study of geometry by focusing on groups of geometric transformations, and properties that are invariant under them. It is opposed to the classical synthetic geometry approach of Euclidean geometry, that focuses on ...

  4. Glide reflection - Wikipedia

    en.wikipedia.org/wiki/Glide_reflection

    In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation. Because the distances between points are not changed under glide reflection, it is a motion or isometry.

  5. Translation surface - Wikipedia

    en.wikipedia.org/wiki/Translation_surface

    Translation surface. In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form . These surfaces arise in dynamical systems where they can be used to model billiards, and in ...

  6. Isometry - Wikipedia

    en.wikipedia.org/wiki/Isometry

    Translation T is a direct isometry: a rigid motion. [1] In mathematics, an isometry (or congruence, or congruent transformation) is a distance -preserving transformation between metric spaces, usually assumed to be bijective. [a] The word isometry is derived from the Ancient Greek: ἴσος isos meaning "equal", and μέτρον metron meaning ...

  7. Similarity (geometry) - Wikipedia

    en.wikipedia.org/wiki/Similarity_(geometry)

    Similarity (geometry) In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.

  8. Translation of axes - Wikipedia

    en.wikipedia.org/wiki/Translation_of_axes

    Translation of axes. In mathematics, a translation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x'y' -Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away. This means that the origin O' of the new ...

  9. Translational symmetry - Wikipedia

    en.wikipedia.org/wiki/Translational_symmetry

    According to Noether's theorem, space translational symmetry of a physical system is equivalent to the momentum conservation law. Translational symmetry of an object means that a particular translation does not change the object. For a given object, the translations for which this applies form a group, the symmetry group of the object, or, if ...

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