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  2. Reflection (mathematics) - Wikipedia

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

    Point Q is the reflection of point P through the line AB. In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a perpendicular from the point to the line (plane) used for reflection, and extend it the same distance on the other side. To find the reflection of a figure, reflect each point in the figure.

  3. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Transformation of coordinates (a,b) when shifting the reflection angle in increments of When the direction of a Euclidean vector is represented by an angle θ , {\displaystyle \theta ,} this is the angle determined by the free vector (starting at the origin) and the positive x {\displaystyle x} -unit vector.

  4. Rotations and reflections in two dimensions - Wikipedia

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

    The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...

  5. 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.

  6. Mirrors and Reflections - Wikipedia

    en.wikipedia.org/wiki/Mirrors_and_Reflections

    Mirrors and Reflections is aimed at undergraduate mathematics students, and uses an intuitive and heavily visual approach suitable for that level. [1] [2] [3] its readers are expected to already have a solid background in linear algebra and some group theory.

  7. Method of images - Wikipedia

    en.wikipedia.org/wiki/Method_of_images

    A quick way to model this reflection is with the method of images. The reflections, or images, are oriented in space such that they perfectly replace any mass (from the real plume) passing through a given boundary. [3] A single boundary will necessitate a single image. Two or more boundaries produce infinite images.

  8. Reflection symmetry - Wikipedia

    en.wikipedia.org/wiki/Reflection_symmetry

    In mathematics, reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2-dimensional space, there is a line/axis of symmetry, in 3-dimensional space, there is a plane of symmetry.

  9. Motion (geometry) - Wikipedia

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

    A glide reflection is a type of Euclidean motion.. In geometry, a motion is an isometry of a metric space.For instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping associating congruent figures is a motion. [1]

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