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Forum Geometricorum

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    The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2012volume12/FG201224index.html The editors Forum
    Message 1 of 476 , Nov 30, 2012
      The following paper has been published in Forum Geometricorum. It can be viewed at

      http://forumgeom.fau.edu/FG2012volume12/FG201224index.html

      The editors
      Forum Geometricorum
      Harold Reiter and Arthur Holshouser, Using complex weighted centroids to create homothetic polygons,
      Forum Geometricorum, 12 (2012) 247--254.

      Abstract. After first defining weighted centroids that use complex arithmetic, we then make a simple observation which proves Theorem 1. We next define complex homothety. We then show how to apply this theory to triangles (or polygons) to create endless numbers of homothetic triangles (or polygon). The first part of the paper is fairly standard. However, in the final part of the paper, we give two examples which illustrate that examples can easily be given in which the simple basic underpinning is so disguised that it is not at all obvious. Also, the entire paper is greatly enhanced by the use of complex arithmetic.


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    • forumgeom forumgeom
      The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html The editors Forum
      Message 476 of 476 , Apr 16 8:32 AM
        The following paper has been published in Forum Geometricorum. It can be viewed at

        http://forumgeom.fau.edu/FG2013volume13/FG201309ndex.html

        The editors
        Forum Geometricorum

        Paul Yiu, On the conic through the intercepts of the three lines through the centroid and the intercepts of a given line,
        Forum Geometricorum, 13 (2013) 87--102.

        Abstract. Let L be a line intersecting the sidelines of triangle ABC at X, Y, Z respectively. The lines joining these intercepts to the centroid give rise to six more intercepts on the sidelines which lie on a conic Q(L,G). We show that this conic (i) degenerates in a pair of lines if L is tangent to the Steiner inellipse, (ii) is a parabola if L is tangent to the ellipse containing the trisection points of the sides, (iii) is a rectangular hyperbola if L is tangent to a circle C_G with center G. We give a ruler and compass construction of the circle C_G. Finally, we also construct the two lines each with the property that the conic Q(L,G) is a circle.


        [Non-text portions of this message have been removed]
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