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The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
In physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center.
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.
However, other methods have also been proposed or used to determine the centres of various countries and regions. These include: centroid of volume (incorporating elevations into calculations), instead of the more usual centroid of area as described above. [6] centre point of a bounding box completely enclosing the area. While relatively easy ...
the mean center, also known as the centroid or center of gravity; the median center, which is the intersection of the median longitude and median latitude; the geometric median, also known as Weber point, Fermat–Weber point, or point of minimum aggregate travel. A further complication is caused by the curved shape of the Earth.
Shift of the world's economic center of gravity since 1980 and projected until 2050 [7] Various definitions of geographical centres exists. The definitions used by the references in this article refer to calculations within the 2 dimensions of a surface, mainly as the surface of Earth is the domain of human cultural existence.
A circle is divided into 360 degrees; subdivisions of the degree include the minute (1 ⁄ 60 of one degree) and the second (1 ⁄ 3600 of one degree). Degrees are commonly used to divide the roughly spherical shape of the Earth for geographic and cartographic purposes, e.g. when reporting latitudes and longitudes. [1] degree day
A cyclic polygon has each of its vertices on a particular circle, called the circumcircle or circumscribed circle. The centre of the circumcircle, called the circumcentre, can be considered a centre of the polygon. If a polygon is both tangential and cyclic, it is called bicentric. (All triangles are bicentric, for example.) The incentre and ...