Back to the previously mentioned question: “How is it possible to play chess on a spherical chessboard with the traditional rules?” To answer that, first I need to exhaustively display all 64 squares on the surface of Dot in a 2-dimensional diagram, so I can draw pictures to explain it well.
It takes two steps to make a diagram of Dot:
1) Divide the Dot into two hemispheres by splitting it from the equator.
2) Use “Azimuthal equidistant projection” to project them as two circles.
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| Make a diagram of Dot |
In the diagram, the upper circle is the northern hemisphere and the lower circle is the southern hemisphere.
The circumferences of two circles are connected with a single point on the diagram, but they are actually full-connected as a Dot (the equator of Dot). The animation below shows the relation of squares on two hemispheres more accurately.
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| The relation of squares on two hemispheres |
In the future, consider the circles of all diagrams are rotatable, just like the gear-wheel animation above.
To be continued.
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