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PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
A stadium is a two-dimensional geometric shape constructed of a rectangle with semicircles at a pair of opposite sides. [1] The same shape is known also as a pill shape, [2] discorectangle, [3] obround, [4] [5] or sausage body. [6] The shape is based on a stadium, a place used for athletics and horse racing tracks.
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
Another use of elliptical distributions is in robust statistics, in which researchers examine how statistical procedures perform on the class of elliptical distributions, to gain insight into the procedures' performance on even more general problems, [20] for example by using the limiting theory of statistics ("asymptotics").
Body of constant width (yellow) formed by intersecting disks (blue) centered on a semi-ellipse (black). The red circle shows a tangent circle to a supporting line, at a point of minimum curvature of the semi-ellipse. The eccentricity of the semi-ellipse in the figure is the maximum possible for this construction.
Hemihelix, a quasi-helical shape characterized by multiple tendril perversions; Tendril perversion (a transition between back-to-back helices) Seiffert's spiral; Slinky spiral; Space cardioid; Twisted cubic; Viviani's curve
Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes . Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics, such as 3D modeling, by its emphasis on physical fidelity. [1]