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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.
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"
Area#Area formulas – Size of a two-dimensional surface; Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities
The difference equation for the G-function, in conjunction with the functional equation for the gamma function, can be used to obtain the following reflection formula for the Barnes G-function (originally proved by Hermann Kinkelin):
Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, [a] which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental ...
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).
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The major accomplishment of Hippocrates is that he was the first to write a systematically organized geometry textbook, called Elements (Στοιχεῖα, Stoicheia), that is, basic theorems, or building blocks of mathematical theory. From then on, mathematicians from all over the ancient world could, at least in principle, build on a common ...
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