Isometric deformations of planar quadrilaterals with constant index

E. S. Zaputryaeva

Moscow State Pedagogical University

Abstract: We consider isometric deformations (motions) of polygons (so-called carpenter's rule problem) in the case of self-intersecting polygons with the additional condition that the index of the polygon is preserved by the motion. We provide general information about isometric deformations of planar polygons and give a complete solution of the carpenter's problem for quadrilaterals.
Bibliography: 17 titles.

Keywords: planar polygons, linkages, carpenter's rule problem.

UDC: 514.772.35

MSC: 51E12

Received: 13.07.2013 and 27.11.2013

DOI: 10.4213/sm8270

 English version: Sbornik: Mathematics, 2014, 205:5, 663–683

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