4 papers
Complex invariants of poristic Steiner 4-chains
Ana Diakvnishvili, Giorgi Khimshiashvili
We are concerned with the Steiner chains consisting of four circles. More precisely, we deal with the so-called complex moments of Steiner 4-chains introduced in a recent paper by…
Hooke and Coulomn Energy of Tripod Spiders
Giorgi Khimshiashvili, Dirk Siersma
Tripod spiders are the simplest examples of arachnoid mechanisms. Their workspaces and configuration spaces are well known. For Hooke potential, we give a complete description of t…
Area-perimeter duality in polygon spaces
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail…
Extremal areas of polygons with fixed perimeter
Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma
We consider the configuration space of planar -gons with fixed perimeter, which is diffeomorphic to the complex projective space . The oriented area function…