  We develop a uniform method to derive Chudnovsky-Ramanujan type formulae for
triangle groups based on a generalization of a method of Chudnovsky and
Chudnovsky; in particular, we carry out the method systematically for
non-compact arithmetic triangle groups and one non-Fuchsian covering. As a
result, we derive all rational Ramanujan type series given by Chan-Cooper for
levels 1-4, as well as two additional rational series of a similar form
prescribed by Chan-Cooper for these levels, but not found in the paper of
Chan-Cooper. These two additional series were first found by Z.-W. Sun in a
slightly different form. We also derive additional rational series of a similar
form, but not found in the papers of Chan-Cooper nor Z.-W. Sun. As an
ingredient in the method, we give an algorithm to rigorously confirm the
singular values of normalized Eisenstein series of weight 2, which may be of
independent interest.
