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  2. Truncus (mathematics) - Wikipedia

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

    The basic truncus y = 1 / x 2 has asymptotes at x = 0 and y = 0, and every other truncus can be obtained from this one through a combination of translations and dilations. For the general truncus form above, the constant a dilates the graph by a factor of a from the x -axis; that is, the graph is stretched vertically when a > 1 and compressed ...

  3. Dilation (metric space) - Wikipedia

    en.wikipedia.org/wiki/Dilation_(metric_space)

    [1] In Euclidean space, such a dilation is a similarity of the space. [2] Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point [3] that is called the center of dilation. [4] Some congruences have fixed points and others do not. [5]

  4. Dilation (morphology) - Wikipedia

    en.wikipedia.org/wiki/Dilation_(morphology)

    Dilation (usually represented by ⊕) is one of the basic operations in mathematical morphology. Originally developed for binary images, it has been expanded first to grayscale images, and then to complete lattices. The dilation operation usually uses a structuring element for probing and expanding the shapes contained in the input image.

  5. Mathematical morphology - Wikipedia

    en.wikipedia.org/wiki/Mathematical_morphology

    Mathematical Morphology was developed in 1964 by the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France.Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and ...

  6. Homothety - Wikipedia

    en.wikipedia.org/wiki/Homothety

    k = −1 corresponds to a point reflection at point S Homothety of a pyramid. In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number k called its ratio, which sends point X to a point X ′ by the rule, [1]

  7. Homothetic center - Wikipedia

    en.wikipedia.org/wiki/Homothetic_center

    Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center. In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another.

  8. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Shape Area Perimeter/Circumference Meanings of symbols Square: is the length of a side Rectangle (+)is length, is breadth Circle: or : where is the radius and is the diameter ...

  9. Length contraction - Wikipedia

    en.wikipedia.org/wiki/Length_contraction

    Kleinian Geometry Euclidean plane: Galilean plane: Minkowski plane Symbol E 2: E 0,1: E 1,1: Quadratic form Positive definite: Degenerate: Non-degenerate but indefinite Isometry group E(2) E(0,1) E(1,1) Isotropy group SO(2) SO(0,1) SO(1,1) Type of isotropy Rotations: Shears: Boosts Algebra over R Complex numbers: Dual numbers: Split-complex ...

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