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Geometry Of 3-Dimensions Problem


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#1 SaxonViolence

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Posted 12 June 2019 - 06:48 PM

Friends,

 

Take a checkered game board—like a chess board, but probably with more squares.

 

Now if I stipulate that I don't care how much the former squares get distorted...

 

Is there a way to wrap the board around a sphere in such a way that I preserve all of my rows, columns and diagonals?

 

I've seen "Spherical" chess sets, but they're more distorted cylinders without full coverage or connectivity over the top and bottom.

 

 

…..Saxon Violence



#2 SaxonViolence

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Posted 13 June 2019 - 03:06 PM

Yeah!

 

I write—though not very successfully.

 

I wanted a chess variant in one of my stories, where the game surface is on a virtual sphere—no supplemental views or note-taking allowed. The Sphere is rolled about virtually and a big part of the difficulty is remembering and picturing the hemisphere that you cannot see.

 

By the way, it's called "Sphess" for "Spherical Chess."

 

Thanks.

 

Except the "Squares" at the very top are triangles.

 

HMMMmmnnn...

 

Looking at the diagram, it seems that what I want is physically impossible. As the squares shrink towards the pole, eventually we are forced to a point.

 

I think a better question might be...

 

Can we imagine a bunch of four-sided figures connected topologically like the squares in a round chessboard—but in every direction?

 

And can we further write a program to show Half of this surface on a monitor at one time, in the shape of a hemisphere?

 

We literally can't have a Sphess board in the material world because it isn't physically possible in 3-D...