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

Triangle geometry of the qubit state in the probability representation expressed in terms of the triada of Malevich's Squares