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A solid square is understood to be two-dimensional; if such a figure is rep-tiled into pieces each scaled down by a factor of 1/3 in both dimensions, there are a total of 3 2 = 9 pieces. We see that for ordinary self-similar objects, being n-dimensional means that when it is rep-tiled into pieces each scaled down by a scale-factor of 1/ r ...
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in - dimensional Euclidean space. [ 1 ]
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [2] It was popularized in English by Hugo Steinhaus in the 1950 edition of his book Mathematical ...
Pattern Blocks are a set of mathematical manipulatives developed in the 1960s. The six shapes are both a play resource and a tool for learning in mathematics, which serve to develop spatial reasoning skills that are fundamental to the learning of mathematics. Among other things, they allow children to see how shapes can be composed and ...
The following is a list of second moments of area of some shapes. The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not ...
An irregular volume in space can be approximated by an irregular triangulated surface, and irregular tetrahedral volume elements. In numerical analysis , complicated three-dimensional shapes are commonly broken down into, or approximated by, a polygonal mesh of irregular tetrahedra in the process of setting up the equations for finite element ...