# The Magic Square 3x3 and 9x9 matrixes X3 up to Infinity

“If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”

― **Nikola Tesla**

“If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.”

― **Nikola Tesla**

Creating a base 3 magic square with equivalency in rows, columns, diagonals, and area.

A simple geometric pattern is completely unlimited in size and application.

A simple example, the 3x3 matrix is perhaps a very old, important, and powerful pattern hidden in plain sight. The numbers themselves reveal the relative position and sequence populating the matrix. These positions indicate the numbers within a 3x3 matrix, the position of a 3x3 matrix within a 9x9 matrix, the position of a 9x9 matrix within a 27x27 matrix continuing onward. All of the squares on this website strictly adhere to this pattern.

The 9x9 matrix . Composed of 9 - 3x3 matrix. Following the simple pattern in the 3x3 the 9x9 can be populated many different ways.

Just a random sampling of other fill patterns used in a 9x9 matrix.

The 27x27 composed of 9 - 9x9's with 9 - 3x3's each occupying 9 positions.

- The core matrix is the individual matrix which can be a 3x3 , 9x9, 27x27 etc. using any of the fill patterns strictly adhering to the central pattern. Copies of the core matrix when aligned comprise a layer.
- The core matrix above is a 9x9 matrix. The 9x9 matrix is positioned in 9 layers on the Z Axis.
- A 3x3 matrix will have 3 layers on the Z-Axis, a 9x9 has 9 layers , an 81x81 has 81 layers etc.
- Each successive layer must be transposed by 1 position on the x- axis or on the y axis.
- The shifting of the layers is always performed in the same direction and each layer is shifted progressively by 1 position per layer.
- There is no limit to the maximum size of the x, y, or z axis. (The z-axis is based on the core matrix size, the core matrix size is not limited.)
- The core matrices are aligned side by side and end to end and extend indefinitely. The area or size of the core matrix can be focused anywhere, the sums in the x, y and z axis in that area of focus will be equivalent just like the Magic Square.
- If the outside edges of a column or row were brought together (producing a round tube ) the sums on the X, Y , and Z axis surrounding that connecting line would be seamless as no line would exist there at all.
- An Excel Spreadsheet with a sample 9x9x9 Magic cube is located in the Download section.

This 9x9x9 Magic Cube - 9 Magic squares of 1 to 81 stacked to produce 9 columns of equivalent sums of 369. Only 1 layer in the cube can have equivalent diagonals. On this one I arranged it to be Layer 5.

The average value of the squares surrounding the center square is the value of the center square.

An Excel spreadsheet with this Magic cube is located in the down load section.

The resulting fill in the 3x3's are incremented x9 in the 1-3, 4-6, and 7-9 positions.

Watch a 9x9 being filled using the most basic fill pattern. You will see each 3x3 matrix is filled in sequence and the 3x3's occupy the 9x9 using the same sequence.

Watch a 9x9 being filled in 3 cell increments within the 3x3 and 9x9 matrixes. You will see each 3x3 matrix is filled in sequence and the 3x3's occupy the 9x9 using the same sequence.

Watch a 9x9 being filled in 3 cell increments within the 3x3 and 9 cell increments in the 9x9 matrixes. You will see each 3x3 matrix is filled in sequence and the 3x3's occupy the 9x9 using the same sequence. A cool feature of this pattern is that the diagonal from the upper left to the lower right is sequential.

1 of 36 different fill patterns for the X3 or X9fill process.

A 6561x6561 Magic Square at 1 square inch per number the dimensional size is greater than 1-1/2 football fields square with 1,625,702,400 different solutions. That is for a x9 type fill and the number is tripled to 4,877,107,200 solutions when you include 2 methods for a x3 type fill.

The 6561 is an 8th order matrix (3 raised to the 8th power). The number of permutations for 8 using 8 is 40,320 combinations. Since the row and column positions can be cojoined independently while strictly adhering to the simple pattern for each, there are 40,320 combinations for the rows and 40,320 combinations for columns which render 1,625,702,400 different patterns (solutions)in a x9 type fill.

A website about discovering the properties of the 3x3 magic square and seeing how that pattern expands infinitely into magic squares of incalculable precision and size.

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