@NatVoltaic Best I've got is that a diagonal is basically moving in multiple dimensions. In 2D, it's the only 2 you've got, x and y. In 3D, it could be along 2 (xy, yz, xz) or 3 (xyz) dimensions. Extend that out to 4D (xy, xz, xw, yz, yw, zw, xyz, xyw, xzw, yzw, xyzw), and you get the general ways a bishop moves, then use the added constraint that a bishops moves the same number of spaces in all dimensions it moves in (if it moves ±3 in x, it moves ±3 in y) to get the exact moves.