Abstract
Our universe is threedimensional and curved (with a positive curvature) and thus may be embedded in a fourdimensional Euclidean space with coordinates x, y, z, t where the fourth dimension time t is treated as a regular dimension. One can set in this spacetime a fourdimensional underlying array of small hypercubes of one Planck length edge. With this array all elementary particles can be classified following that they are two, three or fourdimensional. The elementary wavefunctions of this underlying array are equal to √ 2exp ix i for x i = x, y, z or to √ 2exp it for t. Hence, the masses of the fermions of the first family are equal to 2 n (in eV/c 2) where n is an integer. The other families of fermions are excited states of the fermions of the first family and thus have masses equal to 2 n .p 2 /2 where n and p are two integers. Theoretical and experimental masses fit within 10%.