ANY CYCLIC QUADRILATERAL CAN BE INSCRIBED IN ANY CLOSED CONVEX SMOOTH CURVE

DOI10.1017/fms.2018.7zbMath1395.53001arXiv1712.10205OpenAlexW2780527175MaRDI QIDQ4563967

Sergey Avvakumov, Arseniy V. Akopyan

Publication date: 5 June 2018

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.10205

zbMATH Keywords

quadrilateralconvex curverectangle

Mathematics Subject Classification ID

Fixed points and coincidences in algebraic topology (55M20) Convex sets in (2) dimensions (including convex curves) (52A10) Curves in Euclidean and related spaces (53A04)

Related Items (11)

Families of similar simplices inscribed in most smoothly embedded spheres ⋮ Four Lines and a Rectangle ⋮ On the square peg problem and its relatives ⋮ A trichotomy for rectangles inscribed in Jordan loops ⋮ Pushing a rectangle down a path ⋮ SPLITTING LOOPS AND NECKLACES: VARIANTS OF THE SQUARE PEG PROBLEM ⋮ Inscribed rectangle coincidences ⋮ Fun problems in geometry and beyond ⋮ Configuration spaces, multijet transversality, and the square-peg problem ⋮ Quadrilaterals inscribed in convex curves ⋮ Rectangles, curves, and Klein bottles

Cites Work

• Unnamed Item
• A note on Makeev's conjectures
• Rectangles inscribed in symmetric continua
• Quadrangles inscribed in a closed curve
• On simplexes inscribed in a hypersurface
• A Survey on the Square Peg Problem
• The Topology of Square Pegs in Round Holes
• Inscribed squares and square‐like quadrilaterals in closed curves
• AN INTEGRATION APPROACH TO THE TOEPLITZ SQUARE PEG PROBLEM
• Inscribing cubes and covering by rhombic dodecahedra via equivariant topology
• Quadrilaterals inscribed in convex curves

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