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dc.contributor.authorCoghetto, Roland-
dc.date.accessioned2017-05-16T09:30:37Z-
dc.date.available2017-05-16T09:30:37Z-
dc.date.issued2016-
dc.identifier.citationFormalized Mathematics, Volume 24, Issue 1, pp. 27-36pl
dc.identifier.issn1426-2630pl
dc.identifier.issn1898-9934pl
dc.identifier.urihttp://hdl.handle.net/11320/5488-
dc.description.abstractWe introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.-
dc.language.isoen-
dc.publisherDe Gruyter Open-
dc.subjectEuclidean geometry-
dc.subjecttrigonometry-
dc.subjectaltitude-
dc.subjectorthocenter-
dc.subjecttriangulation-
dc.subjectdistance-
dc.titleAltitude, Orthocenter of a Triangle and Triangulation-
dc.typeArticle-
dc.identifier.doi10.1515/forma-2016-0003-
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.-
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dc.description.referencesRoland Coghetto. Some facts about trigonometry and Euclidean geometry. Formalized Mathematics, 22(4):313-319, 2014. doi:10.2478/forma-2014-0031.-
dc.description.referencesRoland Coghetto. Morley’s trisector theorem. Formalized Mathematics, 23(2):75-79, 2015. doi:10.1515/forma-2015-0007.-
dc.description.referencesRoland Coghetto. Circumcenter, circumcircle and centroid of a triangle. Formalized Mathematics, 24(1):19-29, 2016. doi:10.1515/forma-2016-0002.-
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dc.description.referencesAkihiro Kubo. Lines on planes in n-dimensional Euclidean spaces. Formalized Mathematics, 13(3):389-397, 2005.-
dc.description.referencesAkihiro Kubo. Lines in n-dimensional Euclidean spaces. Formalized Mathematics, 11(4): 371-376, 2003.-
dc.description.referencesAkihiro Kubo and Yatsuka Nakamura. Angle and triangle in Euclidean topological space. Formalized Mathematics, 11(3):281-287, 2003.-
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.-
dc.description.referencesBoris A. Shminke. Routh’s, Menelaus’ and generalized Ceva’s theorems. Formalized Mathematics, 20(2):157-159, 2012. doi:10.2478/v10037-012-0018-9.-
dc.description.referencesAndrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.-
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