  We determine the charge radius of the proton by analyzing the published low
momentum transfer electron-proton scattering data from Mainz. We note that
polynomial expansions of the form factor converge for momentum transfers
squared below $4m_\pi^2$, where $m_\pi$ is the pion mass. Expansions with
enough terms to fit the data, but few enough not to overfit, yield proton radii
smaller than the CODATA or Mainz values and in accord with the muonic atom
results. We also comment on analyses using a wider range of data, and overall
obtain a proton radius $R_E=0.840(16$) fm.
