09 - Longitudinal Loop

Continue with the previous article.

If an aircraft on planet Earth flies along longitude and keeps its route straight, it will reach a pole, and then another pole, and then eventually back to its starting point.

Likewise, if a piece, e.g., a rook, on square d7 on the Dot moves along longitude and keeps its route straight, it will pass d8, N, h8, h7, h6, h5, h4, h3, h2, h1, S, d1, d2, d3, d4, d5, d6 and eventually move back to d7.

Rook moves along longitude on the Dot

Now if I change the diagram above into the 2DFARCSOD below, it will look like this:

Rook moves along longitude on the Dot

Like previously mentioned, all rooks on the 2DFARCSOD above are actually the same one, because all chessboards are in fact replicas from the single, original one.

And here is the single-chessboard view:

Rook moves along longitude on the Dot

Due to the “North-South reversed” of some chessboards, the moving direction of piece is also North-South reversed when it pass the pole.

To be continued.