Meanings of closer approximation in English

A closer approximation to our ideal may be found in a story related by the Persian poet Saadi (358):

It grows, also, by the closer approximation of all the members one to another, and the individual increase of each in Christlike characteristics.

With a little practice in estimating the last drop, we may, in trying to estimate the density of water, even reach a closer approximation.

Marilyn Liebermann was a much closer approximation to the all-American girl than Rachel, with blonde flick-ups, a big pink-lipped smile and a generous figure.

Rather, the poet proudly maintains, they are infinitely superior, being in fact closer approximations to the meaning of things than are the things themselves.