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The following is an example of applying a continuity correction. Suppose one wishes to calculate Pr( X ≤ 8) for a binomial random variable X . If Y has a distribution given by the normal approximation, then Pr( X ≤ 8) is approximated by Pr( Y ≤ 8.5).
The definitions and results in this section are taken from the 1913 text Plane and Solid Geometry by George A. Wentworth and David Eugene Smith (Wentworth & Smith 1913).. A cylindrical surface is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line.
A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction, , and , and primed angles ′ indicate the ray's angle after refraction.. Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the element and using Snell's law at each interface.
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Given n lines L and a point P(L) on each line, find the locus of points Q such that the lengths of the line segments QP(L) satisfy certain conditions. For example, when n = 4, given the lines a, b, c, and d and a point A on a, B on b, and so on, find the locus of points Q such that the product QA*QB equals the product QC*QD.
Esotropia (from Greek eso 'inward' and trope 'a turning' [1]) is a form of strabismus in which one or both eyes turn inward. The condition can be constantly present, or occur intermittently, and can give the affected individual a "cross-eyed" appearance. [2]
The formula for vertex correction is = (), where F c is the power corrected for vertex distance, F is the original lens power, and x is the change in vertex distance in meters. Derivation [ edit ]
The resulting equation is of 4th order but, unlike Euler–Bernoulli beam theory, there is also a second-order partial derivative present. Physically, taking into account the added mechanisms of deformation effectively lowers the stiffness of the beam, while the result is a larger deflection under a static load and lower predicted ...