2019/11/21 by Irina Busjatskaja, Busjatskaja, Irina, Yury Kochetkov +1 · 1 citation
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Finite Group Theory Research #Metric Geometry (math.MG) #graph theory and CDMA systems #math.MG
paper · pdf · doi:10.48550/arxiv.1911.09321
9 pages, 9 figures
arxiv created 2019/11/21 · openalex publication_date 2019/11/21 · arxiv updated 2019/11/22 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28
We consider quadrangles of perimeter 2 in the plane with marked directed edge. To such quadrangle Q a two-dimensional plane Π∈ℝ4 with orthonormal base is corresponded. Orthogonal plane Π^\bot defines a plane quadrangle Q^∘ of perimeter 2 and with marked directed edge. This quadrangle is defined uniquely (up to rotation and symmetry). Quadrangles Q and Q^∘ will be called dual to each other. The following properties of duality are proved: a) duality preserves convexity, non convexity and self-intersection; b) duality preserves the length of diagonals; c) the sum of lengths of corresponding edges in Q and Q^∘ is 1.