These images showcase a complex mathematical structure known as Mahmood's Rhombus Math Magic 20x20. This is essentially a specialized form of a Magic Square, but presented through a geometric tiling of rhombuses rather than a standard grid.
Here is a breakdown of the "magic" properties displayed in the magic grid:
1. The Magic Sum (4010)
In the first image, you’ll notice the number 4010 listed at the end of every row and the bottom of every column. This is the Magic Constant.
- The grid contains all integers from 1 to 400.
- Since there are 20 rows/columns, the average sum per line is 4,010
2. Rhombus Clusters (3208)
The subsequent images highlight a different property. Each "large" rhombus is actually a cluster of 8 smaller triangles/diamonds.
- The Constant 3208: In these diagrams, the creator has grouped 16 of these small segments into color-coded patterns.
- Notice how the number 3208 is placed in the white space between the colored clusters. This indicates that any highlighted group of 16 numbers in that specific pattern also sums to exactly 3208.
3. Structural Variations
The different images demonstrate that this "Magic" isn't static. By shifting or rotating the patterns (as seen in the movement of colors between images 3,4), the mathematical balance remains intact.
- Symmetry: The numbers are distributed using high-level modular arithmetic to ensure that no matter how you "slice" the grid (rows, columns, or specific geometric clusters), the sum remains predictable.
- Visual Patterns: The color coding helps visualize how the numbers 1… 400 are balanced—high numbers are systematically paired with low numbers to maintain the equilibrium.
Note: These are extremely difficult to construct manually and usually require computer algorithms or complex "knights move" tiling patterns to ensure every row, column, and sub-section balances out perfectly.
