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  2. Reflection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Reflection_(mathematics)

    A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in ...

  3. Dihedral group - Wikipedia

    en.wikipedia.org/wiki/Dihedral_group

    The dihedral group D 2 is generated by the rotation r of 180 degrees, and the reflection s across the x-axis. The elements of D 2 can then be represented as {e, r, s, rs}, where e is the identity or null transformation and rs is the reflection across the y-axis. The four elements of D 2 (x-axis is vertical here) D 2 is isomorphic to the Klein ...

  4. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where

  5. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and ...

  6. Template:Frieze group notations - Wikipedia

    en.wikipedia.org/wiki/Template:Frieze_group...

    (TRHVG) Horizontal and Vertical reflection lines, Translations and 180° Rotations: This group requires three generators, with one generating set consisting of a translation, the reflection in the horizontal axis and a reflection across a vertical axis.

  7. Frieze group - Wikipedia

    en.wikipedia.org/wiki/Frieze_group

    Any transformation of the plane leaving this pattern invariant can be decomposed into a translation, (x, y) ↦ (n + x, y), optionally followed by a reflection in either the horizontal axis, (x, y) ↦ (x, −y), or the vertical axis, (x, y) ↦ (−x, y), provided that this axis is chosen through or midway between two dots, or a rotation by ...

  8. Here’s What to Say to Comfort Someone Who Just Had a ... - AOL

    www.aol.com/heres-comfort-someone-just-had...

    They’re pretty common, with about 23 million miscarriages happening across the world every year, or about 44 losses a minute, based on a 2021 study in the weekly medical publication Lancet Journal.

  9. Glide reflection - Wikipedia

    en.wikipedia.org/wiki/Glide_reflection

    This isometry maps the x-axis to itself; any other line which is parallel to the x-axis gets reflected in the x-axis, so this system of parallel lines is left invariant. The isometry group generated by just a glide reflection is an infinite cyclic group. [1]