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Broken Space Diagonal
In a magic cube, a broken space diagonal is a sequence of cells of the cube that follows a line parallel to a space diagonal of the cube, and continues on the corresponding point of an opposite face whenever it reaches a face of the cube. Broken space diagonals are also known as broken triagonals.. The corresponding concept in two-dimensional magic squares is a broken diagonal In recreational mathematics and the theory of magic squares, a broken diagonal is a set of ''n'' cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of as wrapping around the boundaries of the squa .... References Magic squares {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Cube
In mathematics, a magic cube is the dimension, 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an ''n'' × ''n'' × ''n'' pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal to the same number, the so-called magic constant of the cube, denoted ''M''3(''n''). It can be shown that if a magic cube consists of the numbers 1, 2, ..., ''n''3, then it has magic constant :M_3(n) = \frac. If, in addition, the numbers on every cross section (geometry), cross section diagonal also sum up to the cube's magic number, the cube is called a perfect magic cube; otherwise, it is called a semiperfect magic cube. The number ''n'' is called the order of the magic cube. If the sums of numbers on a magic cube's broken space diagonals also equal the cube's magic number, the cube is called a pandiagonal magic cube. Alternative definition In recen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space Diagonal
In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with '' face diagonals'', which connect vertices on the same face (but not on the same edge) as each other. For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals. Axial diagonal An axial diagonal is a space diagonal that passes through the center of a polyhedron. For example, in a cube with edge length ''a'', all four space diagonals are axial diagonals, of common length a\sqrt . More generally, a cuboid with edge lengths ''a'', ''b'', and ''c'' has all four space diagonals axial, with common length \sqrt. A regular octahedron has 3 axial diagonals, of length a\sqrt , with edge length ''a''. A regular icosahedron has 6 axial diagonals of length a\sqrt , where \varphi is the golden ratio (1+\sqrt 5)/2.. Space dia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Broken Diagonal
In recreational mathematics and the theory of magic squares, a broken diagonal is a set of ''n'' cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of as wrapping around the boundaries of the square to form a single sequence. In pandiagonal magic squares A magic square in which the broken diagonals have the same sum as the rows, columns, and diagonals is called a pandiagonal magic square. Examples of broken diagonals from the number square in the image are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4. The fact that this square is a pandiagonal magic square can be verified by checking that all of its broken diagonals add up to the same constant: : 3+12+14+5 = 34 : 10+1+7+16 = 34 : 10+13+7+4 = 34 One way to visualize a broken diagonal is to imagine a "ghost image" of the panmagic square adjacent to the original: The set of numbers of a broken diagonal, wrapped around the original square, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
