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Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, [1] algebra, [2] geometry, [1] and analysis, [3 ...
Solomonoff's theory of inductive inference is a mathematical theory of induction introduced by Ray Solomonoff, based on probability theory and theoretical computer science. [1] [2] [3] In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data.
A worksheet, in the word's original meaning, is a sheet of paper on which one performs work. They come in many forms, most commonly associated with children's school work assignments, tax forms, and accounting or other business environments. Software is increasingly taking over the paper-based worksheet. It can be a printed page that a child ...
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays: propagate in straight ...
v. t. e. Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') [1] is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. [2] Geometry is, along with arithmetic, one of ...
where = / is the ray index – that is, the refractive index calculated on the ray velocity instead of the usual phase velocity (wave-normal velocity). For an infinitesimal path, we have d S = n r d s , {\displaystyle dS=n_{\mathrm {r} \,}ds\,,\,} indicating that the optical length is the physical length multiplied by the ray index: the OPL is ...
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