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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 fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
Line fitting is the process of constructing a straight line that has the best fit to a series of data points. Several methods exist, considering: Vertical distance: Simple linear regression; Resistance to outliers: Robust simple linear regression
The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere. The counterparts of a circle in other dimensions can never be packed with complete efficiency in dimensions larger than one (in a one-dimensional universe, the circle analogue is just two points). That is ...
A replica of an apparatus used by Geiger and Marsden to measure alpha particle scattering in a 1913 experiment. The Rutherford scattering experiments were a landmark series of experiments by which scientists learned that every atom has a nucleus where all of its positive charge and most of its mass is concentrated.
The three possible line-sphere intersections: 1. No intersection. 2. Point intersection. 3. Two point intersection. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all; Intersection in exactly one point; Intersection in two points.
Some instances of the smallest bounding circle. The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.
They are a generalization of the concept of a straight line in the plane. For the sphere the geodesics are great circles. Many other surfaces share this property. Of all the solids having a given volume, the sphere is the one with the smallest surface area; of all solids having a given surface area, the sphere is the one having the greatest volume.
When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius , or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed ...