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Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In an -dimensional space a Gaussian function can be defined as = (), where = [] is a column of coordinates, is a positive-definite matrix, and denotes matrix transposition. The integral of this Gaussian function over the whole n {\displaystyle n} -dimensional space is given as ∫ R n exp ( − x T C x ) d x = π n det C ...
ALGLIB has an implementations in C++ / C# / VBA / Pascal. GSL has a polynomial interpolation code in C; SO has a MATLAB example that demonstrates the algorithm and recreates the first image in this article; Lagrange Method of Interpolation — Notes, PPT, Mathcad, Mathematica, MATLAB, Maple; Lagrange interpolation polynomial on www.math-linux.com
Angular field of view is typically specified in degrees, while linear field of view is a ratio of lengths. For example, binoculars with a 5.8 degree (angular) field of view might be advertised as having a (linear) field of view of 102 mm per meter. As long as the FOV is less than about 10 degrees or so, the following approximation formulas ...
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
Increasingly, macro photography is accomplished using compact digital cameras and small-sensor bridge cameras, combined with a high powered zoom lens and (optionally) a close-up diopter lens added to the front of the camera lens. The deep depth of field of these cameras is an advantage for macro work.
The American Petroleum Institute gravity, or API gravity, is a measure of how heavy or light a petroleum liquid is compared to water: if its API gravity is greater than 10, it is lighter and floats on water; if less than 10, it is heavier and sinks.
In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation.