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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate point ( x , y , z ) {\displaystyle (x,y,z)} within the local axial rectangular prism linearly, using function data on the lattice points.
In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a plane , the normal component of a force , the normal vector , etc.
A monkey's fist knot is essentially a 3-dimensional representation of the Borromean rings, albeit with three layers, in most cases. [41] Sculptor John Robinson has made artworks with three equilateral triangles made out of sheet metal, linked to form Borromean rings and resembling a three-dimensional version of the valknut.
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [ 1 ] [ 2 ] [ 3 ] On an expression or formula calculator , one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
The resulting four-dimensional points may be projected back into three-space with a perspective divide. In general, operations on a rational curve (or surface) are equivalent to operations on a nonrational curve in a projective space. This representation as the "weighted control points" and weights is often convenient when evaluating rational ...
The first step amounts to analysis of hypothesized representations resulting in a tentative classification. The second step is actual realization of these representations. A real Lie algebra is usually complexified enabling analysis in an algebraically closed field. Working over the complex numbers in addition admits nicer bases.
To do this, for each in , a measuring element that is typically a 2-dimensional square or 3-dimensional box with side length corresponding to is used to scan a pattern or data set (e.g., an image or object) according to a predetermined scanning plan to cover the relevant part of the data set, recording, i.e.,counting, for each step in the scan ...