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AREA OF TRIANGLES ASSOCIATED WITH A CURVE

  • Kim, Dong-Soo (Department of Mathematics Chonnam National University) ;
  • Shim, Kyu-Chul (Department of Mathematics Chonnam National University)
  • Received : 2013.05.28
  • Published : 2014.05.31

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 study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas.

Keywords

triangle;area;parabola;strictly convex curve;plane curvature

References

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Cited by

  1. ON TRIANGLES ASSOCIATED WITH A CURVE vol.52, pp.3, 2015, https://doi.org/10.4134/BKMS.2015.52.3.925
  2. Area properties associated with a convex plane curve vol.24, pp.3, 2017, https://doi.org/10.1515/gmj-2016-0027
  3. Center of Gravity and a Characterization of Parabolas vol.55, pp.2, 2015, https://doi.org/10.5666/KMJ.2015.55.2.473
  4. Areas associated with a Strictly Locally Convex Curve vol.56, pp.2, 2016, https://doi.org/10.5666/KMJ.2016.56.2.583
  5. AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE vol.37, pp.1, 2015, https://doi.org/10.5831/HMJ.2015.37.1.41
  6. CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE vol.52, pp.2, 2015, https://doi.org/10.4134/BKMS.2015.52.2.571