Pascal like triangles and Sierpinski like gaskets
Tomohide Hashiba, Yuta Nakagawa, Toshiyuki Yamauchi, Hiroshi Matsui, Satoshi Hashiba, Daisuke Minematsu, Munetoshi Sakaguchi, Ryohei Miyadera (2007)
Visual Mathematics
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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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Liping Yuan, Carol T. Zamfirescu (2007)
Bollettino dell'Unione Matematica Italiana
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Motivated by various applications triangulations of surfaces using only acute triangles have been recently studied. Triangles and quadrilaterals can be triangulated with at most 7, respectively 10, acute triangles. Doubly covered triangles can be triangulated with at most 12 acute triangles. In this paper we investigate the acute triangulations of doubly covered convex quadrilaterals, and show that they can be triangulated with at most 20 acute triangles.
Roland Coghetto (2016)
Formalized Mathematics
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We 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.
C. Cherfils, F. Hermeline (1990)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Paulus Gerdes (2003)
Visual Mathematics
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Mirzoev, Tigran, Vassilev, Tzvetalin (2010)
Serdica Journal of Computing
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We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2...
Schulze, Bernd (2011)
The Electronic Journal of Combinatorics [electronic only]
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Čerin, Zvonko (2000)
Mathematica Pannonica
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Dawson, Robert J. MacG., Doyle, Blair (2006)
The Electronic Journal of Combinatorics [electronic only]
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Fevens, Thomas, Hernandez, Antonio, Mesa, Antonio, Morin, Patrick, Soss, Michael, Toussaint, Godfried (2001)
Beiträge zur Algebra und Geometrie
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Bukor, József (2008)
Annales Mathematicae et Informaticae
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Mark Keil, J, Vassilev, Tzvetalin (2010)
Serdica Journal of Computing
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* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005. We consider sets of points in the two-dimensional Euclidean plane. For a planar point set in general position, i.e. no three points collinear, a triangulation is a maximal set of non-intersecting straight line segments with vertices in the given points. These segments, called edges, subdivide the convex hull of the set into triangular regions called...