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The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three- dimensional ( solid figures ), although many of its tools and principles can be applied to sets of any finite dimension.
In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. [1] It consists of a sequence of "staircase" polygonal chains in a unit square , formed from horizontal and vertical line segments of decreasing length, so that these staircases converge uniformly to ...
The second step is discretization, where the weak form is discretized in a finite-dimensional space. After this second step, we have concrete formulae for a large but finite-dimensional linear problem whose solution will approximately solve the original BVP. This finite-dimensional problem is then implemented on a computer.
3D curves — Example 01 3D curves — Example 02. Geometrical design (GD) is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumes [1] and is closely related to geometric modeling. Core problems are curve and surface modelling and representation.
Many of these problems are easily solvable provided that other geometric transformations are allowed; for example, neusis construction can be used to solve the former two problems. In terms of algebra, a length is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a ...