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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"
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.
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.
The duplication matrix is the unique (+) matrix which, for any ... The explicit formula for calculating the duplication matrix for a ...
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 ...
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]
Things seem fairly set for the College Football Playoff, but some different scenarios could play out this weekend. A look at all the possibilities.
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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