  We show that the charge radii of neighboring atomic nuclei, independent of
atomic number and charge, follow remarkably very simple relations, despite the
fact that atomic nuclei are complex finite many-body systems governed by the
laws of quantum mechanics. These relations can be understood within the picture
of independent-particle motion and by assuming neighboring nuclei having
similar pattern in the charge density distribution. A root-mean-square (rms)
deviation of 0.0078 fm is obtained between the predictions in these relations
and the experimental values, i.e., a comparable precision as modern
experimental techniques. Such high accuracy relations are very useful to check
the consistence of nuclear charge radius surface and moreover to predict
unknown nuclear charge radii, while large deviations from experimental data is
seen to reveal the appearance of nuclear shape transition or coexsitence.
