The secret power of the diagonals

In the previous article, The Hidden Geography of the Chessboard, I explored the meaning of the squares, the importance of the central ones and how they affect the game. However, the battle for the control of the board does not stop there. Like the 'squares', every 'line' has its strategic role.

Continuing our exploration of the chessboard geometry, I will talk about the lines of movement, in particular — the diagonals — and their crucial impact on the game. Diagonals are oblique lines defined as consecutive squares that touch from corner to corner and have the characteristic of being squares of the same color. For this reason, a Bishop moving along the diagonals cannot control the entire chessboard but only half of it, limiting its range of action 🎯.

Looking at the chessboard, the diagonals can have different lengths: for example, by placing a bishop in one of the 4 central squares, they tend to be symmetrical, and the maximum number of squares that can be obtained is 13. Moving away from the center, this number decreases, with a minimum of 7 from any external square. As we get closer to the edges of the board, the diagonals become asymmetrical and influence the control of the game differently.

This shows that the strength of a piece is not only in its position but also in the directions in which it can act. Let's step back on the initial consideration of bishop limits, one might also ask: what is the minimum number of bishops needed to control the entire board? 🤔

Surprisingly, four bishops are required to dominate the dark squares and, symmetrically, another four for the light squares. 🤯 💣

In conclusion, the diagonals transform the field with their ability to cut across the chessboard, offering players powerful tools to get control and pressure from unexpected angles.

Alberto