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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]
Note: In this algorithm January and February are counted as months 13 and 14 of the previous year. E.g. if it is 2 February 2010 (02/02/2010 in DD/MM/YYYY), the algorithm counts the date as the second day of the fourteenth month of 2009 (02/14/2009 in DD/MM/YYYY format) So the adjusted year above is:
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 ...
The f-number N is given by: = where f is the focal length, and D is the diameter of the entrance pupil (effective aperture).It is customary to write f-numbers preceded by "f /", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N. [1]
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
The chain-ladder or development [1] method is a prominent [2] [3] actuarial loss reserving technique. The chain-ladder method is used in both the property and casualty [1] [4] and health insurance [5] fields.
The Sony FE 90mm F2.8 Macro G OSS is a full-frame macro prime lens for the Sony E-mount, announced by Sony on 4 March 2015.. As of June 2017, the 90mm Macro lens is one of only 3 E-mount lenses manufactured by Sony that are specifically designed for macro photography, with the others being the Sony FE 50mm F2.8 Macro and Sony E 30mm F3.5 Macro lenses.
Another refinement of the notion of a field is a topological field, in which the set F is a topological space, such that all operations of the field (addition, multiplication, the maps a ↦ −a and a ↦ a −1) are continuous maps with respect to the topology of the space. [40]