Cyclic polygons are critical points of area

DOI10.1007/s10958-009-9417-zzbMath1193.52015OpenAlexW1974371555MaRDI QIDQ1037004

G. N. Khimshiashvili, Gaiane Yu. Panina

Publication date: 13 November 2009

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-009-9417-z

Mathematics Subject Classification ID

Other designs, configurations (05B30) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Characteristic classes and numbers in differential topology (57R20) Discriminantal varieties and configuration spaces in algebraic topology (55R80)

Related Items (20)

Point charges and polygonal linkages ⋮ Extremal area of polygons, sliding along a circle ⋮ Extremal connectors for disjoint circles ⋮ Unnamed Item ⋮ Area, perimeter and cocyclical polygons ⋮ Complex geometry of polygonal linkages ⋮ Critical configurations of planar robot arms ⋮ Moduli spaces of bicentric quadrilaterals ⋮ Extremal areas of polygons with fixed perimeter ⋮ On the area of constrained polygonal linkages ⋮ Centered configurations of open linkages ⋮ Critical configurations of planar multiple penduli ⋮ Swap action on moduli spaces of polygonal linkages ⋮ Polygons with prescribed edge slopes: configuration space and extremal points of perimeter ⋮ Oriented area is a perfect Morse function ⋮ Morse index of a cyclic polygon ⋮ Extremal configurations of robot arms in three dimensions ⋮ Coulomb control of polygonal linkages ⋮ Oriented area as a Morse function on polygon spaces ⋮ Morse index of a cyclic polygon. II

Cites Work

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• Configuration spaces and signature formulas
• On the geometry of the planar 4-bar mechanism
• Areas of polygons inscribed in a circle
• Universality theorems for configuration spaces of planar linkages
• Rigidity and polynomial invariants of convex polytopes
• On configuration spaces of planar pentagons
• Inscribed polygons and Heron polynomials

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