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Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, dn, between points. [ 1] To convert between these two formulations of the problem ...
Curve fitting. Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss–Newton algorithm with variable damping factor α). Curve fitting[1][2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [4][5] Curve ...
Mathematical analysis of 2D packing of circles (2022). H C Rajpoot from arXiv "The best known packings of equal circles in a circle (complete up to N = 2600)" "Online calculator for "How many circles can you get in order to minimize the waste?"
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated packing density, η, of an ...
The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. [1][2][3]
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the ...
Engineering fits are generally used as part of geometric dimensioning and tolerancing when a part or assembly is designed. In engineering terms, the "fit" is the clearance between two mating parts, and the size of this clearance determines whether the parts can, at one end of the spectrum, move or rotate independently from each other or, at the other end, are temporarily or permanently joined.