One dimensional map of the world?

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Bit of a strange question but hope this is OK to ask here.

Has anyone heard of a '1-dimensional' projection of the world map - that is mapping all the points on the globe to a single line?

I was thinking of doing such a thing - trying to keep cities that are 'close' on the globe 'close' on the line.

Before I do this, I wondered what the state of the art might be in this area?



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