Jump to Magic cubes based on Dürer's and Gaudi Magic squares - A magic cube can be built with the constraint of a given magic square. (c) If we allow negative integers, then various small magic squares of cubes are known with null magic sums, using similar tricks as first published in my 4x4. GEOMETRIC MAGIC SQUARES AND CUBES. The term "geometric" has been applied to that class of magic squares wherein the numbers in the different rows.
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Paracelsus' contemporary Heinrich Cornelius Agrippa von Nettesheim published his famous book De occulta philosophia inwhere he devoted a magic squares and cubes to the planetary squares shown below. The same set of squares given by Agrippa reappear in in Practica Arithmetice by Girolamo Cardano.
The tradition of planetary squares was continued into the 17th century by Athanasius Kircher in Oedipi Aegyptici I think magic squares and cubes 4x4 are also impossible with distinct positive cubes. The 12x12 WT1 trimagic square of part 7 below, when its numbers are cubed, is a magic square of cubes.
A square consisting of consecutive numbers starting with 1 is sometimes known as a "normal" magic square. The unique normal square of order three was known to the ancient Chinese, who called it the Lo Shu.
Magic squares and cubes squares of order 3 through 8 are shown above.
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The magic constant for an th order general magic square starting with an integer and with entries in an increasing arithmetic series with difference between terms is Hunter and Madachy It is an unsolved problem to determine the number of magic squares of an arbitrary order, but the number of distinct magic squares excluding those obtained by rotation and reflection of order2, The number of magic squares was computed by R.
The number of squares is not known, but Pinn and Wieczerkowski estimated it to be using Monte Carlo simulation and methods from statistical mechanics. A tetramagic cube remains a magic squares and cubes cube when the magic squares and cubes are squared, cubed, or raised to the fourth power.