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Pascal's triangle, rows 0 through 7. The hockey stick identity confirms, for example: for n =6, r =2: 1+3+6+10+15=35. In combinatorics , the hockey-stick identity , [ 1 ] Christmas stocking identity , [ 2 ] boomerang identity , Fermat's identity or Chu's Theorem , [ 3 ] states that if n ≥ r ≥ 0 {\displaystyle n\geq r\geq 0} are integers, then
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis. It is named after Paul Scherrer.
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. Its intent is to estimate incurred but not reported claims and project ultimate loss amounts. [5]
Here are given examples of Fraunhofer diffraction with a normally incident monochromatic plane wave. In each case, the diffracting object is located in the z = 0 plane, and the complex amplitude of the incident plane wave is given by A ( x ′ , y ′ ) = a e i 2 π c t / λ = a e i k c t {\displaystyle A(x',y')=ae^{i2\pi ct/\lambda }=ae^{ikct ...
Point pattern analysis (PPA) [1] is the study of point patterns, the spatial arrangements of points in space (usually 2-dimensional space). The simplest formulation is a set X = { x ∈ D } where D , which can be called the 'study region,' is a subset of R n , a n -dimensional Euclidean space .
The Ladder from Hatch Escapes has become one of the most buzzed-about escape rooms in the country, redefining how puzzles can tell stories. This L.A. escape room explores corporate greed — and ...
A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant. [1] It graphically depicts the ratios of the three variables as positions in an equilateral triangle .
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]