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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.
An exercise of elementary analytic geometry shows that in all three cases, both the x - and y-coordinates of the newly defined point satisfy a polynomial of degree no higher than a quadratic, with coefficients that are additions, subtractions, multiplications, and divisions involving the coordinates of the previously defined points (and ...
PGA allows projection, meet, and angle formulas to be derived from (,,) - with a very minor extension to the algebra it is also possible to derive distances and joins. PGA is a widely used system that combines geometric algebra with homogeneous representations in geometry, but there exist several other such systems.
In geometry, the mirror image of an object or two-dimensional figure is the virtual image formed by reflection in a plane mirror; it is of the same size as the original object, yet different, unless the object or figure has reflection symmetry (also known as a P-symmetry).
The duplication matrix is the unique (+) matrix which, for any symmetric matrix, transforms () into (): = ().For the symmetric matrix = [], this transformation reads
This is a list of human anatomy mnemonics, categorized and alphabetized.For mnemonics in other medical specialties, see this list of medical mnemonics.Mnemonics serve as a systematic method for remembrance of functionally or systemically related items within regions of larger fields of study, such as those found in the study of specific areas of human anatomy, such as the bones in the hand ...
A better estimate is provided by the total area of the cross-sections perpendicular to the muscle fibers (green lines in figure 1). This measure is known as the physiological cross-sectional area (PCSA), and is commonly calculated and defined by the following formula, developed in 1975 by Alexander and Vernon: [4] [5] [6]