Dividing the Sides of a Triangle in Proportional Parts
Paulus Gerdes (2003)
Visual Mathematics
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Paulus Gerdes (2003)
Visual Mathematics
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Čerin, Z. (1997)
Mathematica Pannonica
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Bukor, József (2008)
Annales Mathematicae et Informaticae
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Čerin, Zvonko (2000)
Mathematica Pannonica
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Tomohide Hashiba, Yuta Nakagawa, Toshiyuki Yamauchi, Hiroshi Matsui, Satoshi Hashiba, Daisuke Minematsu, Munetoshi Sakaguchi, Ryohei Miyadera (2007)
Visual Mathematics
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Brunat, Josep M., Maureso, Montserrat (2011)
Integers
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Diane M. Donovan, James G. Lefevre, Thomas A. McCourt, Nicholas J. Cavenagh (2012)
Commentationes Mathematicae Universitatis Carolinae
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We define a proper triangulation to be a dissection of an integer sided equilateral triangle into smaller, integer sided equilateral triangles such that no point is the vertex of more than three of the smaller triangles. In this paper we establish necessary and sufficient conditions for a proper triangulation of a convex region to exist. Moreover we establish precisely when at least two such equilateral triangle dissections exist. We also provide necessary and sufficient conditions for...
Stammler, Ludwig (1997)
Beiträge zur Algebra und Geometrie
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Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Roland Coghetto (2016)
Formalized Mathematics
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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...
Kynčl, Jan, Tancer, Martin (2008)
The Electronic Journal of Combinatorics [electronic only]
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