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  2. Inversion (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inversion_(discrete...

    An inversion may be denoted by the pair of places (2, 4) or the pair of elements (5, 2). The inversions of this permutation using element-based notation are: (3, 1), (3, 2), (5, 1), (5, 2), and (5,4). In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order.

  3. Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Inversive_geometry

    This is called circle inversion or plane inversion. The inversion taking any point P (other than O ) to its image P ' also takes P ' back to P , so the result of applying the same inversion twice is the identity transformation which makes it a self-inversion (i.e. an involution).

  4. Reciprocal polynomial - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_polynomial

    This is used in the special number field sieve to allow numbers of the form x 11 ± 1, x 13 ± 1, x 15 ± 1 and x 21 ± 1 to be factored taking advantage of the algebraic factors by using polynomials of degree 5, 6, 4 and 6 respectively – note that φ (Euler's totient function) of the exponents are 10, 12, 8 and 12.

  5. Octahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Octahedral_symmetry

    An object with this symmetry is characterized by the part of the object in the fundamental domain, for example the cube is given by z = 1, and the octahedron by x + y + z = 1 (or the corresponding inequalities, to get the solid instead of the surface). ax + by + cz = 1 gives a polyhedron with 48 faces, e.g. the disdyakis dodecahedron.

  6. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    [1] Assuming that has an inverse in a neighbourhood of and that its derivative at that point is non-zero, its inverse is guaranteed to be differentiable at and have a derivative given by the above formula. The inverse function rule may also be expressed in Leibniz's notation. As that notation suggests,

  7. No. 4 South Carolina, coming off rare loss, uses 32-0 run to ...

    www.aol.com/no-4-south-carolina-coming-205404253...

    No. 4 South Carolina went on a 32-0 run in the first half and beat No. 15 Iowa State 76-36 in the Fort Myers Tip-Off on Thursday. The Gamecocks — playing for the first time since now-No. 1 UCLA ...

  8. Rotations and reflections in two dimensions - Wikipedia

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

    A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.

  9. What is impoundment? How Trump thinks he can control spending ...

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    A version of this story appeared in CNN’s What Matters newsletter. To get it in your inbox, sign up for free here. “Impoundment” is another word that Americans may need to learn in the ...

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