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

Part of: Fiber spaces and bundles Classical differential geometry Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  31 May 2018

ARSENIY AKOPYAN  and
SERGEY AVVAKUMOV
ARSENIY AKOPYAN
Affiliation:
Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria; akopjan@gmail.com, s.avvakumov@gmail.com
SERGEY AVVAKUMOV
Affiliation:
Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria; akopjan@gmail.com, s.avvakumov@gmail.com

Abstract

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We prove that any cyclic quadrilateral can be inscribed in any closed convex $C^{1}$-curve. The smoothness condition is not required if the quadrilateral is a rectangle.

MSC classification

Primary: 53A04: Curves in Euclidean space 55M20: Fixed points and coincidences
Secondary: 55R80: Discriminantal varieties, configuration spaces
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e7
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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