  The Garvey-Kelson relations (GKRs) are algebraic expressions originally
developed to predict nuclear masses. In this letter we show that the GKRs
provide a fruitful framework for the prediction of other physical observables
that also display a slowly-varying dynamics. Based on this concept, we extend
the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out
of the approximately 800 nuclei whose charge radius is experimentally known. We
find a rms deviation between the GK predictions and the experimental values of
only 0.01 fm. This should be contrasted against some of the most successful
microscopic models that yield rms deviations almost three times as large.
Predictions - with reliable uncertainties - are provided for 116 nuclei whose
charge radius is presently unknown.
