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Given these two expressions

1) $\sinh{d}=\frac{\sqrt{t^2−x^2}}{\sqrt{1−(t^2−x^2)}}$

2) $\sin{d}=\frac{\sqrt{t^2−x^2}}{\sqrt{1+(t^2−x^2)}}$

for distance $d$ from the origin $(0,0)$ to point $(x,t)$, which of these two options applies to de-Sitter space and which to anti de-Sitter space? For definiteness, assume $t$ is time and $(x,t)$ is time-like, that is $t^2-x^2$ is positive.

Does option (1) correspond to a space with the positive curvature and (2) to the negative one?

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    @Vectornaut $t$ and $x$ are coordinates of $\mathbb R^2$, there is no $z$. The question is about 2d spaces only and I do not use the 3d models you are referring to.2016-01-03

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