Loading ...
Sorry, an error occurred while loading the content.

Forum Geometricorum

Expand Messages
  • forumgeom forumgeom
    The following paper has been published in Forum Geometricorum. It can be viewed at http://forumgeom.fau.edu/FG2011volume11/FG201127index.html The editors Forum
    Message 1 of 476 , Nov 30, 2011
    View Source
    • 0 Attachment
      The following paper has been published in Forum Geometricorum. It can be viewed at

      http://forumgeom.fau.edu/FG2011volume11/FG201127index.html

      The editors
      Forum Geometricorum

      Paul Yiu, Rational Steiner porism,
      Forum Geometricorum, 11 (2011) 237--249.

      Abstract. We establish formulas relating the radii of neighboring circles in a Steiner chain, a chain of mutually tangent circles each tangent to two given ones, one in the interior of the other. From such we parametrize, for n = 3, 4, 6, all configurations of Steiner n-cycles of rational radii.


      [Non-text portions of this message have been removed]
    • 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
      View Source
      • 0 Attachment
        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]
      Your message has been successfully submitted and would be delivered to recipients shortly.