Ramanujan-type formulae for $1\mathrm{/}\pi$: the art of translation

We outline an elementary method for proving numerical hypergeometric identities, in particular, Ramanujan-type identities for $1\mathrm{/}\pi$. The principal idea is using algebraic transformations of arithmetic hypergeometric series to translate non-singular points into singular ones, where the required constants can be computed using asymptotic analysis.