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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 732–737
DOI: https://doi.org/10.33048/semi.2020.17.052 (Mi semr1246) 		 
Geometry and topology

Area of a triangle and angle bisectors

A. A. Buturlakinab, S. S. Presnyakovc, D. O. Revinba, S. A. Savindc

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
c Specialized Educational Scientific Center of Novosibirsk State University, 1/1, Pirogova str., Novosibirsk, 630090, Russia
d The Orthodox Gymnasium in the name saint Sergius of Radonezh, 3, Akademicheskaya str., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2020.17.052
Abstract: Consider a triangle $ABC$ with given lengths $l_a,l_b,l_c$ of its internal angle bisectors. We prove that in general, it is impossible to construct a square of the same area as $ABC$ using a ruler and compass. Moreover, it is impossible to express the area of $ABC$ in radicals of $l_a,l_b,l_c$.
Keywords: area of a triangle, angle bisectors, ruler and compass construction, Galois group of a polynomial, algebraic equation, solution in radicals.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-00007
Ministry of Science and Higher Education of the Russian Federation 075-2019-1675
Siberian Branch of Russian Academy of Sciences I.1.1., project № 0314-2016-0001
Funding: The reported study was funded by RFBR and BRFBR, project number 20-51-00007, by Mathematical Center in Akademgorodok under agreement No 075-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation, and by the Program of Fundamental Scientific Research of the SB RAS No. I.1.1., project number 0314-2016-0001.
Received May 6, 2020, published May 31, 2020
Bibliographic databases:
Document Type: Article
UDC: 514.112.3, 512.622
MSC: 51M04, 12F10
Language: English
Citation: A. A. Buturlakin, S. S. Presnyakov, D. O. Revin, S. A. Savin, “Area of a triangle and angle bisectors”, Sib. Èlektron. Mat. Izv., 17 (2020), 732–737
Citation in format AMSBIB
\Bibitem{ButPreRev20}
\by A.~A.~Buturlakin, S.~S.~Presnyakov, D.~O.~Revin, S.~A.~Savin
\paper Area of a triangle and angle bisectors
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 732--737
\mathnet{http://mi.mathnet.ru/semr1246}
\crossref{https://doi.org/10.33048/semi.2020.17.052}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000537774100001}
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