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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 ...
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 ...
In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. In cartesian coordinates therefore the circle would pass through the points (+1,0) and (−1,0) on the x-axis and the points (0,+1) and (0,−1) on the y-axis.
Glide planes are noted in the Hermann–Mauguin notation by a, b or c, depending on which axis the glide is along. (The orientation of the plane is determined by the position of the symbol in the Hermann–Mauguin designation.) If the axis is not defined, then the glide plane may be noted by g. When the glide plane is parallel to the screen ...
The Schwarz function of a curve in the complex plane is an analytic function which maps the points of the curve to their complex conjugates.It can be used to generalize the Schwarz reflection principle to reflection across arbitrary analytic curves, not just across the real axis.
Geometrically speaking, the graph face of an even function is symmetric with respect to the y-axis, meaning that its graph remains unchanged after reflection about the y-axis. Examples of even functions include |x|, x 2, x 4, cos(x), and cosh(x).
The term reflection is loose, and considered by some an abuse of language, with inversion preferred; however, point reflection is widely used. Such maps are involutions, meaning that they have order 2 – they are their own inverse: applying them twice yields the identity map – which is also true of other maps called reflections.
A symmetry group of a frieze group necessarily contains translations and may contain glide reflections, reflections along the long axis of the strip, reflections along the narrow axis of the strip, and 180° rotations. There are seven frieze groups, listed in the summary table. Many authors present the frieze groups in a different order. [1] [2]