Circumcenter, Circumcircle and Centroid of a Triangle

Pole DC	Wartość	Język
dc.contributor.author	Coghetto, Roland	-
dc.date.accessioned	2017-05-16T09:30:36Z	-
dc.date.available	2017-05-16T09:30:36Z	-
dc.date.issued	2016	-
dc.identifier.citation	Formalized Mathematics, Volume 24, Issue 1, pp. 17-26	pl
dc.identifier.issn	1426-2630	pl
dc.identifier.issn	1898-9934	pl
dc.identifier.uri	http://hdl.handle.net/11320/5487	-
dc.description.abstract	We 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.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	Euclidean geometry	-
dc.subject	perpendicular bisector	-
dc.subject	circumcenter	-
dc.subject	circumcircle	-
dc.subject	centroid	-
dc.subject	extended law of sines	-
dc.title	Circumcenter, Circumcircle and Centroid of a Triangle	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2016-0002	-
dc.description.Affiliation	Coghetto Roland - Rue de la Brasserie 5 7100 La Louvière, Belgium	-
dc.description.references	Grzegorz 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.references	Czesław Byliński. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.	-
dc.description.references	H.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967.	-
dc.description.references	Robin Hartshorne. Geometry: Euclid and beyond. Springer, 2000.	-
dc.description.references	Akihiro Kubo. Lines on planes in n-dimensional Euclidean spaces. Formalized Mathematics, 13(3):389-397, 2005.	-
dc.description.references	Marco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16(2): 97-101, 2008. doi:10.2478/v10037-008-0014-2.	-
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