  Recent estimates of the properties of the Crab nebula are used to derive
constraints on the moment of inertia, mass and radius of the pulsar. To this
purpose, we employ an approximate formula combining these three parameters. Our
"empirical formula" I = a(x)MR^2, where x = (M/M_sun)(km/R), is based on
numerical results obtained for thirty theoretical equations of state of dense
matter. The functions a(x) for neutron stars and strange stars are
qualitatively different. For neutron stars a_NS(x) = x/(0.1+2x) for x <= 0.1
(valid for M > 0.2 M_sun) and a_NS(x) = (2/9)(1+5x) for x > 0.1. For strange
stars a_SS(x) = (2/5)(1+x) (not valid for strange stars with crust and M < 0.1
M_sun). We obtain also an approximate expression for the maximum moment of
inertia I_max,45 = (-0.37 + 7.12x_max) (M_max/M_sun)(R_(M_max)/(10 km))^2,
valid for both neutron stars and strange stars. Applying our formulae to the
evaluated values of I_Crab, we derive constraints on the mass and radius of the
pulsar. A very conservative evaluation of the expanding nebula mass, M_neb = 2
M_sun, yields M_Crab > 1.2 M_sun and R_Crab = 10-14 km. Setting the most recent
evaluation ("central value") M_neb = 4.6 M_sun rules out most of the existing
equations of state, leaving only the stiffest ones: M_Crab > 1.9 M_sun, R_Crab
= 14-15 km.
