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Sbornik: Mathematics, 2003, Volume 194, Issue 3, Pages 311–331
DOI: https://doi.org/10.1070/SM2003v194n03ABEH000718 (Mi sm718) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Inscribed polygons and Heron polynomials

V. V. Varfolomeev

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
English version PDF (263 kB) Citations (18)
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DOI: https://doi.org/10.1070/SM2003v194n03ABEH000718
Abstract: Heron's well-known formula expressing the area of a triangle in terms of the lengths of its sides is generalized in the following sense to polygons inscribed in a circle: it is proved that the area is an algebraic function of the lengths of the edges of the polygon. Similar results are proved for the diagonals and the radius of the circumscribed circle. The resulting algebraic equations are studied and elementary geometric applications of the algebraic results obtained are presented.
Received: 04.03.2002
Russian version:
Matematicheskii Sbornik, 2003, Volume 194, Number 3, Pages 3–24
DOI: https://doi.org/10.4213/sm718
Bibliographic databases:
UDC: 513.7
MSC: 51M25, 52A10, 52A38
Language: English
Original paper language: Russian
Citation: V. V. Varfolomeev, “Inscribed polygons and Heron polynomials”, Mat. Sb., 194:3 (2003), 3–24; Sb. Math., 194:3 (2003), 311–331
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:116
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