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A perfect magic cube of order seven was given by A. H. Frost in 1866, and on March 11, 1875, an article was published in the Cincinnati Commercial newspaper on the discovery of a perfect magic cube of order 8 by Gustavus Frankenstein. Perfect magic cubes of orders nine and eleven have also been constructed.
The smallest normal perfect magic cube is order 8; see Perfect magic cube. Nasik; A. H. Frost (1866) referred to all but the simple magic cube as Nasik! C. Planck (1905) redefined Nasik to mean magic hypercubes of any order or dimension in which all possible lines summed correctly.
Despite his deteriorating health, Hendricks continued his work with magic hypercubes, achieving during this time: the first perfect magic tesseract (order 16), in April 1999; the first order 32 perfect magic tesseract; the first inlaid magic tesseract (order 6 with inlaid order 3) in October 1999; and the first bimagic cube (order 25), June 2000.
An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.. In mathematics, a magic cube is the 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 ...
This was A.H. Frost’s original definition of nasik. A nasik magic cube would have 13 magic lines passing through each of its m 3 cells. (This cube also contains 9m pandiagonal magic squares of order m.) A nasik magic tesseract would have 40 lines passing through each of its m 4 cells, and so on.
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 the cube contains 3m simple magic squares of order m. Because the cube contains so many magic squares, it was considered for many years to be "perfect" (although other types ...
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42 is a pronic number, [1] an abundant number [2] as well as a highly abundant number, [3] a practical number, [4] an admirable number, [5] and a Catalan number. [6]The 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane.
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