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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.
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.
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.
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 ...
He has made contributions working on both the square packing problem and the magic tile problem. In 1979 he discovered the optimal known packing of 11 equal squares in a larger square, [ 2 ] and in 2003, along with Christian Boyer , developed the first known magic cube of order 5. [ 3 ]
As such a magic hyperbeam generalises the two dimensional magic rectangle and the three dimensional magic beam, a series that mimics the series magic square, magic cube and magic hypercube. This article will mimic the magic hypercubes article in close detail, and just as that article serves merely as an introduction to the topic.
Proper: A proper magic cube is a magic cube belonging to one of the six classes of magic cube, but containing exactly the minimum requirements for that class of cube. i.e. a proper simple or pantriagonal magic cube would contain no magic squares, a proper diagonal magic cube would contain exactly 3m + 6 simple magic squares, etc. This term was ...
However, there are infinitely many rational triangular numbers, rational generalized pentagonal numbers and rational tetrahedral numbers which are also magic constants of rational order. The term magic constant or magic sum is similarly applied to other "magic" figures such as magic stars and magic cubes. Number shapes on a triangular grid ...