walkington knight diagonals
Image: William Walkington (CC BY-NC-SA 4.0)

The “Lo Shu square” is the 3 × 3 square enclosed in dashed lines at the center of the diagram above. It’s “magic”: Each row, column, and long diagonal (marked in red) sums to 15. William Walkington has discovered a new magic property — imagine rolling the square into a tube (in either direction), and then bending the tube into a torus. And now imagine hopping from cell to cell around the torus with a “knight’s move” — two cells over and one up. (The extended diagram above helps with visualizing this — follow the blue lines.) It turns out that each such path touches three cells, and these cells always sum to 15. So the square is even more magic than we thought.

More info here. (Thanks, William.)