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  2. 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 ...

  3. 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 ...

  4. Rotation of axes in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_of_axes_in_two...

    The old coordinates (x, y, z) of a point Q are related to its new coordinates (x′, y′, z′) by [14] [′ ′ ′] = [⁡ ⁡ ⁡ ⁡] []. Generalizing to any finite number of dimensions, a rotation matrix A {\displaystyle A} is an orthogonal matrix that differs from the identity matrix in at most four elements.

  5. Euclidean plane isometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_plane_isometry

    Reflection. Reflections, or mirror isometries, denoted by F c,v, where c is a point in the plane and v is a unit vector in R 2.(F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c.

  6. 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]

  7. Graphing calculator - Wikipedia

    en.wikipedia.org/wiki/Graphing_calculator

    The on-board BASIC variants in TI graphing calculators and the languages available on the HP-48 series can be used for rapid prototyping by developers, professors, and students, often when a computer is not close at hand. Most graphing calculators have on-board spreadsheets which usually integrate with Microsoft Excel on the computer side.

  8. Point reflection - Wikipedia

    en.wikipedia.org/wiki/Point_reflection

    In Euclidean geometry, the inversion of a point X with respect to a point P is a point X* such that P is the midpoint of the line segment with endpoints X and X*. In other words, the vector from X to P is the same as the vector from P to X*. The formula for the inversion in P is x* = 2p − x. where p, x and x* are the position vectors of P, X ...

  9. Reflection formula - Wikipedia

    en.wikipedia.org/wiki/Reflection_formula

    In mathematics, a reflection formula or reflection relation for a function f is a relationship between f(a − x) and f(x). It is a special case of a functional equation . It is common in mathematical literature to use the term "functional equation" for what are specifically reflection formulae.