  We map the density matrix of the qubit (spin-1/2) state associated with the
Bloch sphere and given in the tomographic probability representation onto
vertices of a triangle determining Triada of Malevich's squares. The three
triangle vertices are located on three sides of another equilateral triangle
with the sides equal to $\sqrt 2$. We demonstrate that the triangle vertices
are in one-to-one correspondence with the points inside the Bloch sphere and
show that the uncertainty relation for the three probabilities of spin
projections +1/2 onto three orthogonal directions has the bound determined by
the triangle area introduced. This bound is related to the sum of three
Malevich's square areas where the squares have sides coinciding with the sides
of the triangle. We express any evolution of the qubit state as the motion of
the three vertices of the triangle introduced and interpret the gates of qubit
states as the semigroup symmetry of the Triada of Malevich's squares. In view
of the dynamical semigroup of the qubit-state evolution, we constructed
nonlinear representation of the group U(2).
