As most of the users here, I spend a considerably amount of my daily time typing in $\LaTeX$. I think that the typing position of the hands, as least for the US layout, should be different from the one suggested for typing plain text. For example, the right hand should lay on the right edge of th...

Let $(X,d)$ be a complete $CAT(0)$ space (also known as a Hadamard space). Let $x\in H$ and $\gamma:[0,1]\to H$ be some geodesic segment issuing from $x$. For $y,z\in H$ (wlog assume $x\neq y\neq z$) let $[y,z]$ denote the geodesic segment connecting $z$ with $y$. For $\alpha\in [0,1]$ let $z_{\...