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2. 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 ...

3. 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 ...

4. Glide reflection - Wikipedia

   en.wikipedia.org/wiki/Glide_reflection

   Glide reflection. A glide reflection is the composition of a reflection across a line and a translation parallel to the line. This footprint trail has glide-reflection symmetry. Applying the glide reflection maps each left footprint into a right footprint and vice versa. In geometry, a glide reflection or transflection is a geometric ...

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 Teichmüller ...

6. Rigid transformation - Wikipedia

   en.wikipedia.org/wiki/Rigid_transformation

   A rigid transformation is formally defined as a transformation that, when acting on any vector v, produces a transformed vector T(v) of the form. T(v) = R v + t. where RT = R−1 (i.e., R is an orthogonal transformation), and t is a vector giving the translation of the origin. A proper rigid transformation has, in addition,

7. Frieze group - Wikipedia

   en.wikipedia.org/wiki/Frieze_group

   Frieze group. In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. The term is derived from architecture and decorative arts, where such repeating patterns are often used. (See frieze.) Frieze patterns can be classified into seven types according to their symmetries.