We describe a geometric picture for the pattern of fermion masses of t
he three generations which is invariant with respect to the renormaliz
ation group below the electroweak scale. Moreover, we predict the uppe
r limit for the ratio between the Dirac masses of the mu and tau neutr
inos, (m(nu mu)/m(nu tau)) less than or equal to (9.6 +/- 0.6) x 10(-3
).