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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. Octahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Octahedral_symmetry

    The four hexagonal cycles have the inversion (the black knot on top) in common. The hexagons are symmetric, so e.g. 3 and 4 are in the same cycle. A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation.

  5. Rotations and reflections in two dimensions - Wikipedia

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

    These equations can be proved through straightforward matrix multiplication and application of trigonometric identities, specifically the sum and difference identities.. 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.

  6. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    Integrating this relationship gives = ′ (()) +.This is only useful if the integral exists. In particular we need ′ to be non-zero across the range of integration. It follows that a function that has a continuous derivative has an inverse in a neighbourhood of every point where the derivative is non-zero.

  7. Improper rotation - Wikipedia

    en.wikipedia.org/wiki/Improper_rotation

    The direct subgroup of S 2n is C n, order n, index 2, being the rotoreflection generator applied twice. For odd n, S 2n contains an inversion, denoted C i or S 2. S 2n is the direct product: S 2n = C n × S 2, if n is odd. For any n, if odd p is a divisor of n, then S 2n/p is a subgroup of S 2n, index p. For example S 4 is a subgroup of S 12 ...

  8. Play Poker Five Card Draw Online for Free - AOL.com

    www.aol.com/.../poker-five-card-draw

    Poker: Five Card Draw. Make the best five-card combination with an opportunity to draw, while enjoying structured betting. By Masque Publishing. Advertisement. Advertisement. all. board. card.

  9. Duality (order theory) - Wikipedia

    en.wikipedia.org/wiki/Duality_(order_theory)

    In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by P op or P d.This dual order P op is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in P op if and only if y ≤ x holds in P.

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