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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
A change in scale is called a scale transformation. The renormalization group is intimately related to scale invariance and conformal invariance, symmetries in which a system appears the same at all scales (self-similarity). [a] As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system.
A linear transformation rotates, stretches, or shears the vectors upon which it acts. Its eigenvectors are those vectors that are only stretched, with neither rotation nor shear. The corresponding eigenvalue is the factor by which an eigenvector is stretched or squished. If the eigenvalue is negative, the eigenvector's direction is reversed. [1]
Conformal linear transformations come in two types, proper transformations preserve the orientation of the space whereas improper transformations reverse it. As linear transformations, conformal linear transformations are representable by matrices once the vector space has been given a basis , composing with each-other and transforming vectors ...
A scale factor of 1 ⁄ 10 cannot be used here, because scaling 160 by 1 ⁄ 10 gives 16, which is greater than the greatest value that can be stored in this fixed-point format. However, 1 ⁄ 11 will work as a scale factor, because the maximum scaled value, 160 ⁄ 11 = 14. 54, fits within this range. Given this set:
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Ian Harding, Lindsay Lohan and Jon Rudnitsky star in 'Our Little Secret.' (Bob Mahoney / Netflix / Courtesy Everett Collection) (©Netflix/Courtesy Everett Collection)
A disgraced 93-year-old New Orleans priest pleaded guilty Tuesday to charges involving the sexual assault of a teenage boy in 1975.