3x3 Magic Square

Even in a small figure where numbers are simply arranged, a single structure quietly breathes. Here, I will calmly list its prototype and the eight forms derived from it as a record.

3x3 Magic Square (Prototype)

6 1 8
7 5 3
2 9 4
The sum of all rows, columns, and diagonals is 15.
A 3x3 magic square using numbers 1-9 once each
mathematically has this form as its only prototype.

8 Derived Forms

(“Visual differences” due to rotation and reflection)

◆ Rotation (4 types)

[Rotation 0°]
6 1 8
7 5 3
2 9 4

[Rotation 90°]
2 7 6
9 5 1
4 3 8

[Rotation 180°]
4 9 2
3 5 7
8 1 6

[Rotation 270°]
8 3 4
1 5 9
6 7 2

◆ Reflection (4 types)

[Horizontal Reflection]
8 1 6
3 5 7
4 9 2

[Vertical Reflection]
2 9 4
7 5 3
6 1 8

[Main Diagonal Reflection]
6 7 2
1 5 9
8 3 4

[Anti-Diagonal Reflection]
4 3 8
9 5 1
2 7 6

There is only one mathematical solution with 5 in the center.
The corners are always odd numbers.

Magic squares quietly demonstrate a “non-wavering structure” and appear as small records.

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The Roots of Magic Squares