REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU

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dc.contributor.authorCoghetto, Roland-
dc.date.accessioned2017-05-16T09:30:36Z-
dc.date.available2017-05-16T09:30:36Z-
dc.date.issued2016-
dc.identifier.citationFormalized Mathematics, Volume 24, Issue 1, pp. 17-26pl
dc.identifier.issn1426-2630pl
dc.identifier.issn1898-9934pl
dc.identifier.urihttp://hdl.handle.net/11320/5487-
dc.description.abstractWe introduce, using the Mizar system [1], some basic concepts of Euclidean geometry: the half length and the midpoint of a segment, the perpendicular bisector of a segment, the medians (the cevians that join the vertices of a triangle to the midpoints of the opposite sides) of a triangle. We prove the existence and uniqueness of the circumcenter of a triangle (the intersection of the three perpendicular bisectors of the sides of the triangle). The extended law of sines and the formula of the radius of the Morley’s trisector triangle are formalized [3]. Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the centroid (the common point of the medians [4]) of a triangle.-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.subjectEuclidean geometry-
dc.subjectperpendicular bisector-
dc.subjectcircumcenter-
dc.subjectcircumcircle-
dc.subjectcentroid-
dc.subjectextended law of sines-
dc.titleCircumcenter, Circumcircle and Centroid of a Triangle-
dc.typeArticle-
dc.identifier.doi10.1515/forma-2016-0002-
dc.description.AffiliationCoghetto Roland - Rue de la Brasserie 5 7100 La Louvière, Belgium-
dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.-
dc.description.referencesCzesław Byliński. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.-
dc.description.referencesH.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967.-
dc.description.referencesRobin Hartshorne. Geometry: Euclid and beyond. Springer, 2000.-
dc.description.referencesAkihiro Kubo. Lines on planes in n-dimensional Euclidean spaces. Formalized Mathematics, 13(3):389-397, 2005.-
dc.description.referencesMarco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16(2): 97-101, 2008. doi:10.2478/v10037-008-0014-2.-
Występuje w kolekcji(ach):Formalized Mathematics, 2016, Volume 24, Issue 1

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