The size of the electron is still mysterious. Quantum electrodynamics (QED) requires a radius of 0, projection theory gives a radius of 0.66943 10^(-16) m and the classical electron radius calculated via the electron's self-energy is given in the literature as 2.82794 10^(-15)m. The main subject of this work was a decided analysis of the equation system for the calculation of the classical electron radius. The following important points could be worked out: a) The factor f42, which was derived in the context of the projection theory, appears in a system of equations from the established physics. b) The classical electron radius is not 2.82794 10-15m but 1.3214098 10-15m (= λCP = smin), and this finding finds a simple explanation in the projection theory. c) The equations for the calculation of the classical electron radius or for the calculation of the Compton wavelength are, after minor transformations, completely congruent with the formulae developed in projection theory for the calculation of the electrostatic field constant ε0 or Planck's quantum of action h. These new findings clearly show that the projection theory is not an abstruse idea resp. exotic physics, but is already inherent in the existing equations of established physics and these only have to be reinterpreted to recognize the true core of our physical reality.