**IP Stanek Innovative Projects Engineering & Knowledge Transfer** - MAGIC MATHEMATICS for innovative Applications in ENGINEERING & Physics, Koblenz, DE, EU + Asia. Unsolved
Matrix problem: 64 unknowns - 76 equations for magic cubes (64-cells). 1st Solution with Computers by W.Trump 2004 (Spectrum Science 2008-2). 1st analytical Solution with Stanek-Algorithm in 2008
(memomasters 2008/09, InTech 2010).

**1. Introduction **

Mathematics is magic. If we can either use one formula for a wide range of applications or the formula itself will produce magic properties. As one of several introductory examples the generally not well known Leibniz formula for calculating determinants in matrix theory will show that both the well known Laplace laws and Sarrus rules for evaluating matrices are only graphically visualised subsets of this ingenious Leibniz formula. Visualising complex formulas and matrix transformations in 2D and 3D as equivalent graphs is a basic method of the main author in this publication. The huge range of fascinating technical

applications based on 2D magic matrices will be sketched: Constant distribution in all directions of numbers, power, energies, element properties, transport, automation, information flows etc or compensation of punctual disturbances without variation of sum of energy or automatic minimization of energy loss remaining constant distribution or both concentration of energies in near field and hiding of energies in far field or solving magic equation systems in mathematics without using back tracking methods etc.

**2. Background **

The extremely complex problem in mathematics of finding a perfect solution of a 4x4x4 - 3D - magic cube (64 unknowns, but 76 equations/conditions) with constant sum in all directions and continuous numbers from 1 to 64 was solved first by the German mathematician W. Trump in the year 2004 (Spectrum of Science, 2008-2): But this world wide first solution of a 4x4x4 magic cube was only based on parallel computations with several computers and extremely time-intensive back-tracking methods with time consuming solution. In contrast to this computer-based solution of 4x4x4 magic cubes in 2004, the Prof. Dr. W. Stanek has shown a new analytical method manually solving this problem during a presentation on German MemoMasters 2008/2009: Using this analytical method for 4x4x4 the manual 3D solution lasts a few minutes - applying this algorithm the solution time with MATLAB® needs only fractions of seconds (ca. 0.01 s). The results of these matrix transformations for magic 64-cells-cubes show two main aspects:

**a.** Extremely fast solution of such matrix problems in 3D by immediate transformation from magic 2D matrices to magic 3D cubes with remaining
central magic properties.

**b.** New idea solving large sets of linear equations (with also determinant-zero-matrix-property) NOT using conventional equation solvers (Gauss-Seidel,
Newton-Raphson etc) and backtracking methods but only simplified geometrical 3D transformations and logic. This
magic math algorithm is shown by visualised graph transformations and underlying equivalent structures in this Magic Matrix InTech open
publication.

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Some web links & graphics as excerpt re R&D for Magic Matrix Theories & multidiscplinary Applications:

.

1. **Aesculap MemoMasters - Mind Festival**: "Dreidimensionale Zahlenkopfnuss" - 64-cells
new Magic Stanek cube > memomasters.de/aktueller-wettbewerb/archiv/item/40-memo-masters-2008.html

2. **Aesculap MemoMasters - Mind Festival:** Graphics -
comparison between analytical Stanek solution and 1st computer solution in 2004 > ** **memomasters.de/images/pdf/2008/mm_stanek_matrix.pdf

3. **INTECH open** publications for **a)** Magic
Math with new applications and **b)** Magic Units & extended
Electrodynamics by W. Stanek and SGU-co-authors (2010) - PDF download of book "Products & Services; from R&D to Final Solutions" including these 2 R&D chapters (brief overview in shown
graphics)

Here download of InTech publication for MAGIC MATHEMATICS with spectrum of computed applications>