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We describe homogeneous sub-Riemannian geodesics for the standard sub-Riemannian structure on the group of proper motions of the plane SE(2). We show that this structure is not geodesically orbital, although the cut time is invariant w.r.t. shift of the initial point along geodesic., Comment: 6 pages, 3 figures. In Russian

We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle space are discussed., Comment: in Russian, 13 pages, 11 figures

The geometric median of a domain is the point that minimises the average distance from itself to the points of the domain. We will give a gradient system of equations that defines the geometric median of a triangular domain and will prove a simple geometric property of the median. This property states that all three average distances from the median to the sides of the triangle are equal. Further we generalise these results to other types of domains and to other types of median like points., Comment: in Russian, 7 pages, 2 figures