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COMPUTATIONAL GEOMETRY IN Heis 3

. Among eight possible geometric structures on three-dimensional manifolds less studied from the dif- ferential geometric point of view are those modelled on the Heisenberg group Heis 3 . We consider the Heisenberg left-invariant metric and use some results on Levi-Civita connection and curvature tensor to present solutions of equa- tions for geodesic lines in the Heisenberg group. Using ”Mathematica” software package we also present drawings of geodesic lines and metric balls in the Heisenberg group.