Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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AREA OF TRIANGLES ASSOCIATED WITH A CURVE II

  • Kim, Dong-Soo (Department of Mathematics Chonnam National University) ;
  • Kim, Wonyong (Department of Mathematics Chonnam National University) ;
  • Kim, Young Ho (Department of Mathematics Kyungpook National University) ;
  • Park, Dae Heui (Department of Mathematics Chonnam National University)
  • Received : 2014.01.23
  • Published : 2015.01.31
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Abstract

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.

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References

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  3. CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE vol.52, pp.2, 2015, https://doi.org/10.4134/BKMS.2015.52.2.571
  4. Center of Gravity and a Characterization of Parabolas vol.55, pp.2, 2015, https://doi.org/10.5666/KMJ.2015.55.2.473