03 - How

Continue with the previous article.

In order to call it briefly, I gave this spherical chessboard a short name, “Dot”.

It takes three steps to transmogrify a traditional, flat chessboard to a Dot:
1) Connect east and west borders, to create a tube.
2) Cover north and south ends, to create a cylinder.
3) Squeeze and bulk it up to a sphere.

This process is similar to transform a Mercator-projection world map into a terrestrial globe, just like the animation below:

The chessboard-Dot transmogrification animation

So, there are still 64 squares, with two extra “ends” on the surface of Dot.

The two ends are labeled “N” and “S”, they are two poles on the Dot. They are not squares, neither are they white nor black (so I use middle gray to color them). They exist to intact the surface of Dot, and keep all squares four-sided.

Since the two poles are not squares, an important principle rises: Pieces must not stay on the poles.

And as long as the poles are meant to intact the surface of Dot, another important principle rises: Pieces may pass the poles when they move.

By the way, the origin of the name “Dot” is from a photograph of planet Earth taken in 1990 by the Voyager 1 space-probe from a record distance of about 3.7 billion miles away from Earth, which is called “Pale Blue Dot”.

To be continued.