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In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, π radians, or a half-turn). It only has one line of symmetry (reflection symmetry).
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 diagram illustrating the great-circle distance (in cyan) and the straight-line distance (in red) between two points P and Q on a sphere.. To see the utility of different notions of distance, consider the surface of the Earth as a set of points.
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.
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.
A standard example is the Reuleaux triangle, the intersection of three circles, each centered where the other two circles cross. [2] Its boundary curve consists of three arcs of these circles, meeting at 120° angles, so it is not smooth , and in fact these angles are the sharpest possible for any curve of constant width.
Hemihelix, a quasi-helical shape characterized by multiple tendril perversions Tendril perversion (a transition between back-to-back helices) Seiffert's spiral [4]
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 ...