what do you call a circle with every number around it?

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this guy

What do you call this Zeno-ish circle? It has every single number around it.

The numbers are placed at $1/4, 3/8, 7/16, 15/36$ and so on.

Basically $2^{n-1}/2^{n+1}$ for the positives, and $-2^{-n-1}/2^{-n+1}$ for the negatives.

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I think you're talking about the projectively extended real line.