Periodic table of the elements and the Thomas–Fermi atom

How the monotonic trend on which the periodicity of the periodic system is superposed is well described by Thomas–Fermi theory is explained. The mathematical structure of the periodicity is elucidated and explained. Algebraic formulas for the key atomic numbers are derived, e.g., the atomic number at which l electrons first appear is given by Z_f(??) = 4 (∑ n²)+1.