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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] Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist, [4] and cubes of orders five and ...
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. [38] This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3.
Euler brick. In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.
Cross-figure. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells. Clues may be mathematical ("the seventh prime number"), use general knowledge ("date of the ...
In geometry, an octahedron ( pl.: octahedra or octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex . A regular octahedron is the dual polyhedron of a cube.
The six classes. Simple: The minimum requirements for a magic cube are: all rows, columns, pillars, and 4 space diagonals must sum to the same value. A simple magic cube contains no magic squares or not enough to qualify for the next class. The smallest normal simple magic cube is order 3. Minimum correct summations required = 3 m2 + 4. Diagonal:
In a diagonal magic cube of order m, [notes 1] all 6 m 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 3 m 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 ...
Multimagic cube. In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their k th powers for 1 ≤ k ≤ P. 2-multimagic cubes are called bimagic, 3-multimagic cubes are called trimagic, and 4-multimagic cubes tetramagic. [1] A P-multimagic cube is said to be semi-perfect if the k th ...
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