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A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets , in some cases based on dubious fits to data. [ 8 ]
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.. More formally, let and be open subsets of .A function : is called conformal (or angle-preserving) at a point if it preserves angles between directed curves through , as well as preserving orientation.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
Brass, Moser, and Pach call it "one of the oldest and most extensively studied geometric questions concerning lattice points". [ 1 ] At most 2 n {\displaystyle 2n} points can be placed, because 2 n + 1 {\displaystyle 2n+1} points in a grid would include a row of three or more points, by the pigeonhole principle .
This approximation, if it exists, is unique and is given by the line that is tangent to the function at the given point , and the slope of the line is the derivative of the function at . A function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } is differentiable at a {\displaystyle a} if the limit
The Taylor series of any polynomial is the polynomial itself.. The Maclaurin series of 1 / 1 − x is the geometric series + + + +. So, by substituting x for 1 − x, the Taylor series of 1 / x at a = 1 is
In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.The determinant of a matrix A is commonly denoted det(A), det A, or | A |.Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.
A NURBS curve. (See also: the animated creation of a NURBS spline.) A NURBS surface. Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces.