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Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration).
This is determined by summing the moments of inertia of the thin discs that can form the sphere whose centers are along the axis chosen for consideration. If the surface of the sphere is defined by the equation [ 23 ] : 1301 x 2 + y 2 + z 2 = R 2 , {\displaystyle x^{2}+y^{2}+z^{2}=R^{2},}
Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.
The class of diagonal magic cubes is the second of the six magic cube classes (when ranked by the number of lines summing correctly), coming after the simple magic cubes. In a diagonal magic cube of order m, [notes 1] all 6m of the diagonals in the m planes parallel to the top, front, and sides of the cube must sum correctly. This means that ...
n H m 1 * n H m 2 : n [k i] m 1 m 2 = n [ [[k i \ m 2] m 1 m 1 n] m 2 + [k i % m 2] m 2] m 1 m 2. Most compounding methods can be viewed as variations of the above, As most qualifiers are invariant under multiplication one can for example place any aspectual variant of n H m 2 in the above equation, besides that on the result one can apply a ...
A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6] The number of different nets for a simple cube is 11 ...
A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same. Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.
In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant. [ 1 ] [ 2 ] [ 3 ]