Search results
Results from the WOW.Com Content Network
In 1939, B. Rosser and R. J. Walker published a series of papers on diabolic (perfect) magic squares and cubes. They specifically mentioned that these cubes contained 13m 2 correctly summing lines. They also had 3m pandiagonal magic squares parallel to the faces of the cube, and 6m pandiagonal magic squares parallel to the space-diagonal planes ...
Hendricks was also an authority on the design of inlaid magic squares and cubes (and in 1999, a magic tesseract). Following his retirement, he gave many public lectures on magic squares and cubes in schools and in-service teacher's conventions in Canada and the northern United States. He also developed a course on magic squares and cubes which ...
In mathematics, a cubical complex (also called cubical set and Cartesian complex [1]) is a set composed of points, line segments, squares, cubes, and their n-dimensional counterparts. They are used analogously to simplicial complexes and CW complexes in the computation of the homology of topological spaces .
In mathematics and statistics, sums of powers occur in a number of contexts: . Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities.
This definition is based on the fact that a pandiagonal magic square has traditionally been called 'perfect', because all possible lines sum correctly. [7] This same reasoning may be applied to hypercubes of any dimension. Simply stated; in an order m magic hypercube, if all possible lines of m cells sum to the magic constant, the hypercube is ...
G(3) is at least 4 (since cubes are congruent to 0, 1 or −1 mod 9); for numbers less than 1.3 × 10 9, 1 290 740 is the last to require 6 cubes, and the number of numbers between N and 2N requiring 5 cubes drops off with increasing N at sufficient speed to have people believe that G(3) = 4; [18] the largest number now known not to be a sum of ...
All but 6 of the oblique squares are 'broken'. This is analogous to the broken diagonals in a pandiagonal magic square. i.e. Broken diagonals are 1-D in a 2-D square; broken oblique squares are 2-D in a 3-D cube. The table shows the minimum lines or squares required for each class (i.e. proper).
In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces. It can be named by its Schläfli symbol {4,3 7}, being composed of three 8-cubes around each 7-face.