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Vladikavkazskii Matematicheskii Zhurnal, 2025, Volume 27, Number 4, Pages 103–108
DOI: https://doi.org/10.46698/o1944-0990-7792-e (Mi vmj986) 		 
One application of Ptolemy's theorem

Yu. G. Nikonorova, D. N. Oskorbinb

a Southern Mathematical Institute of VSC RAS, 53 Vatutin St., Vladikavkaz 362025, Russia
b Moscow Institute of Physics and Technology, 9 Institutsky Per., Dolgoprudny 141701, Russia
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DOI: https://doi.org/10.46698/o1944-0990-7792-e
Abstract: In this paper, we present a simple proof of one result from a recent paper by Yu. G. Nikonorov and O. Yu. Nikonorova, the original proof of which is rather cumbersome and based on the study of polynomial ideals and symbolic computations using a computer. The new proof is based on Ptolemy's theorem on inscribed quadrilaterals. In addition, other properties of inscribed quadrilaterals and related problems are considered.
Key words: convex polygon, convex quadrilateral, extremal problems, inscribed quadrilateral, integer pentagon, perimeter, Ptolemy's theorem.
Received: 25.03.2025
Document Type: Article
UDC: 514.14
MSC: 52A10, 52A40, 52B60
Language: English
Citation: Yu. G. Nikonorov, D. N. Oskorbin, “One application of Ptolemy's theorem”, Vladikavkaz. Mat. Zh., 27:4 (2025), 103–108
Citation in format AMSBIB
\Bibitem{NikOsk25}
\by Yu.~G.~Nikonorov, D.~N.~Oskorbin
\paper One application of Ptolemy's theorem
\jour Vladikavkaz. Mat. Zh.
\yr 2025
\vol 27
\issue 4
\pages 103--108
\mathnet{http://mi.mathnet.ru/vmj986}
\crossref{https://doi.org/10.46698/o1944-0990-7792-e}
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