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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/FG201226index.html The editors Forum
    Message 1 of 476 , Dec 11, 2012
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      The following paper has been published in Forum Geometricorum. It can be viewed at

      http://forumgeom.fau.edu/FG2012volume12/FG201226index.html

      The editors
      Forum Geometricorum
      Wladimir Boskoff, Lucy, H. Odom, and Bogdan Suceava,
      An elementary view of Gromov hyperbolic spaces,
      Forum Geometricorum, 12 (2012) 283--286.

      Abstract. In the most recent decades, metric spaces have been studied from a variety of viewpoints. One of the important characterizations developed in the study of distances is Gromov hyperbolicity. Our goal here is to provide two approachable, but also intuitive examples of Gromov hyperbolic metric spaces. The authors believe that such examples could be of interest to readers interested in advanced Euclidean geometry; such examples are in fact a familiar introduction into coarse geometries. They are both elementary and fundamental. A scholar familiar with concepts like Ptolemy's cyclicity theorem or various geometric loci in the Euclidean plane could find a familiar environment by working with the concepts presented here.


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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, 2013
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        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.


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