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  2. Duplication - Wikipedia

    en.wikipedia.org/wiki/Duplication

    Duplication, or doubling, multiplication by 2; Duplication matrix, a linear transformation dealing with half-vectorization; Doubling the cube, a problem in geometry also known as duplication of the cube; A type of multiplication theorem called the Legendre duplication formula or simply "duplication formula"

  3. Multiplication theorem - Wikipedia

    en.wikipedia.org/wiki/Multiplication_theorem

    The duplication formula and the multiplication theorem for the gamma function are the prototypical examples. The duplication formula for the gamma function is (+) = ().It is also called the Legendre duplication formula [1] or Legendre relation, in honor of Adrien-Marie Legendre.

  4. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.

  5. Duplication and elimination matrices - Wikipedia

    en.wikipedia.org/wiki/Duplication_and...

    The duplication matrix is the unique (+) matrix which, for any ... The explicit formula for calculating the duplication matrix for a ...

  6. Geometric probability - Wikipedia

    en.wikipedia.org/wiki/Geometric_probability

    Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a ...

  7. Replication (statistics) - Wikipedia

    en.wikipedia.org/wiki/Replication_(statistics)

    In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions to support the original claim, which is crucial to confirm the accuracy of results as well as for identifying and correcting the flaws in the original experiment. [1]

  8. College Football Playoff bracket scenarios. Five possible ...

    www.aol.com/college-football-playoff-bracket...

    Things seem fairly set for the College Football Playoff, but some different scenarios could play out this weekend. A look at all the possibilities.

  9. Plücker coordinates - Wikipedia

    en.wikipedia.org/wiki/Plücker_coordinates

    Displacement d (yellow arrow) and moment m (green arrow) of two points x,y on a line (in red). A line L in 3-dimensional Euclidean space is determined by two distinct points that it contains, or by two distinct planes that contain it (a plane-plane intersection).

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