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How to derive Lobachevsky's formula for the angle of parallelism

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3 $begingroup$ I'm lightly studying some non-Euclidean Geometry and in the book I am reading there is no proof or derivation from where the Lobachevsky formula for angle of parallelism comes from: $$Pi(x)=2tan^{-1}left(e^{-x}right)$$ Any help? Thanks P.S. I couldn't find anything by google search either. differential-geometry hyperbolic-geometry noneuclidean-geometry share | cite | improve this question edited Dec 24 '18 at 9:38 Blue 49.4k 8 70 157 asked Jul 21 '16 at 12:37

How to set if else for vim's “set background = ” for light and dark colorschemes?

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1 For themes like One or PaperColor, there are dark and light versions. For dark or light theme, I usually add my own customizations like bracket color, comment color... etc. I tried to combine them so that everytime I set background=dark or light, with an if else statement. I tried the following but it doesn't work. if (set background=dark) """ my own code here endif Please let me know how to go about this and thank you. vimrc colorscheme share | improve this question asked 3 hours ago mle0312 mle0312 29 4