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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.
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.
This also allows the representation of a division of two numbers in geometrical terms, an important feature to reformulate geometrical problems in algebraic terms. More precisely, if two numbers are given as lengths of line segments one can construct a third line segment, the length of which matches the quotient of those two numbers (see diagram).
Diagram of Stewart's theorem. Let a, b, c be the lengths of the sides of a triangle. Let d be the length of a cevian to the side of length a.If the cevian divides the side of length a into two segments of length m and n, with m adjacent to c and n adjacent to b, then Stewart's theorem states that + = (+).
The butterfly theorem is a classical result in Euclidean geometry, which can be stated as follows: [1]: p. 78 Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn; AD and BC intersect chord PQ at X and Y correspondingly. Then M is the midpoint of XY.
Accused rapist rapper Sean "Diddy" Combs hired men to procure participants for his sick "Freak Off'' sex parties -- peddling the orgies as if it was "an honor'' to be asked to them, a targeted ...
In geometry and mathematical biology, a biconcave disc — also referred to as a discocyte [1] — is a geometric shape resembling an oblate spheroid with two concavities on the top and on the bottom. Biconcave discs appear in the study of cell biology, as an approximation to the shape of certain cells, including red blood cells.