Results 1 to 10 of about 850 (91)
Two inequalities about the pedal triangle [PDF]
Journal of Inequalities and Applications, 2018 Two conjectures about the pedal triangle are proved. For the first conjecture, the product of the distances from an interior point to the vertices is mainly considered and a lower bound is obtained by the geometric method.
Fangjian Huang
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SIERPIŃSKI PEDAL TRIANGLES [PDF]
Fractals, 2008 We generalize the construction of the ordinary Sierpiński triangle to obtain a two-parameter family of fractals we call Sierpiński pedal triangles. These fractals are obtained from a given triangle by recursively deleting the associated pedal triangles in a manner analogous to the construction of the ordinary Sierpiński triangle, but their fractal ...
Zhang, Xin-Min +3 more
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Several observations about Maneeals - a peculiar system of lines
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2016 For an arbitrary triangle ABC and an integer n we define points Dn, En, Fn on the sides BC, CA, AB respectively, in such a manner that |AC|n/|AB|n =|CDn|/|BDn|, |AB|n/|BC|n = |AEn|/|CEn|, |BC|n/|AC|n =|BFn|/|AFn|.
Naga Vijay Krishna Dasari, Jakub Kabat
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STROPHOIDS, A FAMILY OF CUBIC CURVES WITH REMARKABLE PROPERTIES
Journal of Industrial Design and Engineering Graphics, 2015 Strophoids are circular cubic curves which have a node with orthogonal tangents. These rational curves are characterized by a series or properties, and they show up as locus of points at various geometric problems in the Euclidean plane: Strophoids are ...
STACHEL Hellmuth
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Proceedings of the Edinburgh Mathematical Society, 1893 The area of the pedal triangle of a given triangle is easily shown by trilinear co-ordinates to bear to that of the original triangle the ratio R2 – S2: 4R2 where S is the distance of the point from the circumcentre of the triangle. A proof, by purely geometrical methods, of this theorem was read before the Society (Proceedings, Vol. III., pp.
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Triangles with Vertices Equidistant to a Pedal Triangle
, 2020 13 pages, 6 ...
Liang, Xuming, Zelich, Ivan
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Points, whose pedal triangles are similar to the given triangle
, 2012 9 pages, 6 ...
Ganchev, Georgi +2 more
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NON-CONVEXITY OF THE DIMENSION FUNCTION FOR SIERPIŃSKI PEDAL TRIANGLES
Fractals, 2010 We disprove the conjecture of the paper by Zhang et al.1 on the Schur-convexity of the dimension function for the family of Sierpiński pedal triangles. We also show that this function is not convex and the related area-ratio function is not concave in their respective domain.
Ding, Jiu, Tang, Yifa
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Linear Triangle Dynamics: The Pedal Map and Beyond
, 2013 We present a moduli space for similar triangles, then classify triangle maps $f$ that arise from linear maps on this space, with the well-studied pedal map as a special case. Each linear triangle map admits a Markov partition, showing that $f$ is mixing, hence ergodic.
Castellano, Claire, Manack, Corey
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On some applications of the pedal line of a triangle [PDF]
Proceedings of the Edinburgh Mathematical Society, 1890 1. Taking the two following known properties of the pedal line of a triangle, viz.:I. The locus of a point, such that the feet of the perpendiculars from, it on the sides of a triangle are collinear, is the circum-circle of the triangle;II. The pedal line bisects the distance between the orthocentre and the corresponding point in the circumference of ...
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