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Menger showed, in the 1926 construction, that the sponge is a universal curve, in that every curve is homeomorphic to a subset of the Menger sponge, where a curve means any compact metric space of Lebesgue covering dimension one; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in ...
Let the percentage of the total mass divided between these two particles vary from 100% P 1 and 0% P 2 through 50% P 1 and 50% P 2 to 0% P 1 and 100% P 2, then the center of mass R moves along the line from P 1 to P 2. The percentages of mass at each point can be viewed as projective coordinates of the point R on this line, and are termed ...
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.
For an equilateral polygon, the circumcenter of mass and center of mass coincide. More generally, the circumcenter of mass and center of mass coincide for a simplicial polytope for which each face has the sum of squares of its edges a constant. [4] The circumcenter of mass is invariant under the operation of "recutting" of polygons.
A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a single point) remains at the origin. In all center-of-momentum frames, the center of mass is at rest , but it is not necessarily at the origin of the coordinate system.
The concept of a center of gravity as distinct from the center of mass is rarely used in applications, even in celestial mechanics, where non-uniform fields are important. Since the center of gravity depends on the external field, its motion is harder to determine than the motion of the center of mass.
The set or string of edges can, for example, be the outer edges of a flat surface or the edges surrounding a 'hole' in a surface. Example of an edge loop on a cube In a stricter sense, an edge loop is defined as a set of edges where the loop follows the middle edge in every 'four way junction'. [ 1 ]
The centre of a circle is the point equidistant from the points on the edge. Similarly the centre of a sphere is the point equidistant from the points on the surface, and the centre of a line segment is the midpoint of the two ends.